Alumni Newsletter

Alumni Newsletter
THE SCHOOL OF
MATHEMATICS
SUMMER 2016
1

Welcome from The Head of School, Peter Duck
Welcome to the summer 2016 edition of the School of Mathematics Alumni Newsletter.
This has been another good year academically for the School. Since last summer, we
have made five new academic appointments, and by the end of the summer, all four
Turing Fellows will have arrived at the School. The Turing Fellowships are funded by a
very generous external donation with the aim of supporting some of the very best
early career mathematicians to work on challenging mathematical problems. I was
recently delighted to learn that eight members of staff had been promoted, including
four to chairs (Andrew Hazel to Professor of Applied Mathematics, Mark Kambites to
Professor of Pure Mathematics, Will Parnell to Professor of Applied Mathematics and
Louise Walker to Professor of Mathematics). All the promotions are well deserved,
and indicative of the quality of our staff.
During the last academic year the School has set up a committee to administer the
Dame Kathleen Ollerenshaw legacy, with a view to attracting leading figures in mathematics
to visiting positions here in Manchester, to further build on our outreach activities, and also to support the annual
Dame Kathleen Ollerenshaw Public Lecture. As you will find on page 23, last year this lecture was given by Marcus du Sautoy,
a lecture that filled the main theatre in University Place. We are delighted that Hannah Fry (also a figure regularly seen
on TV) has agreed to give this year's lecture. If any of our alumni would like to attend, please email Jenny Sloan
(jenny.sloan@manchester.ac.uk).
On 9th March 2016, in association with The British Society for the History of Mathematics, the School celebrated the lives
of three female mathematicians, Hanna Neumann, Phyllis Nicolson and Bertha Swirles, who not only made significant contributions
to science but also lived incredible lives, thus earning themselves a place in the history of mathematics in Manchester.
A number of friends and relatives of these remarkable ladies were able to attend, and the evening concluded with
the naming of three ground floor rooms in the Alan Turing Building, in their honour. Please see the next page for more details
about the event.
The School was greatly saddened to learn of the death of three former members of staff - Mick McCrudden, Eric Watson
and Jack Williams. Obituaries for these former colleagues can be found in this issue. It is always a pleasure to meet our
alumni and from time-to-time we receive requests to visit us - we are always very happy to show our alumni around our
(relatively) new building, and to reminisce over the past. Please let us know if you are passing and would like to drop by!
Keeping Alan Turing’s memory green
Staff and students from across The University of Manchester congregated to plant an apple tree in memory of Alan Turing
on Monday 29th February 2016. Situated outside St. Peter’s Chaplaincy, the ceremony was jointly organised by St. Peter’s
Chaplaincy, the University’s Sustainability Team and ALLOUT (the University’s LGBTQ network), as well as Manchester
City Council.
Following a series of short speeches by Paul Marks-Jones (Equality
and Diversity Advisor), Rev. Terry Biddington (Chaplaincy Coordinator)
and Dr. James Hopkins (Historian and Heritage Manger—to the
right), Turing was toasted with wine, juice and cakes.
The tree that was chosen to mark Alan Turing’s life is a selfpollinating
Malus Domesticus James Grieve, which produces a versatile
fruit that can be used for eating raw, juicing, cooking and cider-making.
While the tree was once grown and sold across Europe,
it cannot tolerate modern supermarket handling, and is now
only grown in gardens and for direct sale to consumers.
2

New Members of Staff
After completing his PhD in
Bordeaux, France, Mawussi
Zounon joined The School of
Mathematics as a Postdoctoral
Research Associate in
January 2016.
In March 2016, Arno Fehm
joined the University as a Lecturer
in Pure Mathematics.
Prior to starting his post, he
worked at Tel Aviv University,
the Hebrew University of Jerusalem
and The University of
Konstanz, Germany.
Neil Walton started in January
2016 as a Senior Lecturer in
Actuarial Science. Before
moving to Manchester, Neil
worked as an Assistant
Professor at The University of
Amsterdam.
In April 2016, Steven Broom
began his Lecturership in Applied
Mathematics. Steven is also
Head of Admissions, Recruitment
and External Relations within the
School of Mathematics at The
University of Manchester.
After working as a Postdoctoral
Researcher at The University
of Zurich, Switzerland,
Alex Watson joined the
School of Mathematics in
September 2015 as a Lecturer
in Actuarial Science.
Alice Thompson began working
as a Lecturer in Applied Mathematics
at the University in February
2016. Before moving to
Manchester, Alice was a Postdoctoral
Research Associate at
Imperial College London.
Celebrating the History of Women in Mathematics at Manchester
In association with The British Society for the History of Women in Mathematics,
the School’s Athena Swan committee hosted ‘Celebrating the History
of Women in Mathematics at Manchester’ on 9th March 2016, in the Alan
Turing Building.
More than 100 people attended the free, public event which celebrated the
professional lives of three female mathematicians who made incredible contributions
to the field of Mathematics at Manchester: Phyllis Nicolson (below
left), Hanna Neumann (below middle) and Bertha Swirles (below right). Staff,
students, visitors and members of Nicolson’s own family attended.
Peter Neumann (Oxford University) delivered a presentation on the life and works of his mother Hanna Neumann. Ruth
Williams (Cambridge University) spoke about the
mathematical contributions and personal life of her
former colleague Bertha Swirles, and David Silvester
and Catherine Powell (The University of Manchester)
delivered a joint presentation on the Crank-Nicolson
method and the life of Phyllis Nicolson.
3

Encouraging Mathematics among Young People
The 2016
Alan Turing
Cryptography
Competition
The School’s annual online Alan Turing Cryptography Competition continues to
grow in popularity with almost 3,400 entrants this year. Sponsored by
Skyscanner, this year’s theme was artificial intelligence and the Turing Test.
The competition is open to all school pupils in Year 11 (or equivalent) and below,
and runs online from January to April each year. Pupils compete with each other
to crack a series of cryptographic challenges whilst having fun, developing their
mathematical skills and (potentially!) winning some exciting prizes!
This year's winners were team ‘DOE' from King Edwards VI Grammar School, Chelmsford.
This year also saw the launch of our new online competition The Dame Kathleen
Ollerenshaw MathsBombe Competition. This is the sister competition of
the Cryptography Competition and is aimed at students in Years 12-13 (or
equivalent).
Running from January to March, competitors had to solve a series of mathematical
puzzles. The puzzles were quirky, fun and are designed to test and develop
students’ mathematical problem-solving skills without being directly related to
the A-Level Maths syllabus. Why not have a try at one of the puzzles (below)?
The 2016 Dame
Kathleen Ollerenshaw
MathsBombe
Competition
Over 1,4000 students took part in MathsBombe. Team ‘Tantalum’ from Saffron Walden County High School in Essex
took home first prize. Both the Alan Turing Cryptography Competition and MathsBombe will run again in January 2017.
The 2016
Alan Turing
Cryptography Day
On Wednesday 27th April 2016 the School
hosted the third annual Alan Turing Cryptography
Day. Sponsored by Skyscanner,
the event follows the closing of the 2016
Alan Turing Cryptography and
MathsBombe competitions.
Nearly 200 pupils, together with teachers,
from schools across the UK took part in a
live cryptography competition. TED speaker
David Low (Skyscanner) gave a short
talk, and Dr Gavin Brown (Computer Science)
presented his lecture, 'The Robots
are NOT coming to kill us!'.
Above: An example of a puzzle used in the 2016 MathsBombe Competition. Starting at any 'M' on the edge and moving one square
horizontally or vertically, how many different ways are there of spelling 'MathsBombe' ? (Answer on next page).
4

Science
The new 2016
Extravaganza
Mathsbombe
Competition
On Saturday 23rd April 2016, the School of Mathematics took part in
the Science Extravaganza at the Trafford Centre to celebrate Manchester’s
crowning as the 2016 European City of Science.
Manchester mathematicians took to intu Trafford Centre to offer visitors of all
ages the chance to take part in fun, immersive and informative scientific activities.
Participants were able to discover first hand how mathematics is relevant
to our everyday lives by learning about the science behind the (seemingly)
simple act of ribbon curling, which proved to be a big hit at the 2016 Big Bang
Fair in Birmingham a month earlier.
Professor Andrew Hazel and Dr. Charles Walkden led the
University’s stand, which engaged with over 80 families.
The aim of this inspiring and expansive free, public event
was not only to showcase the University’s pioneering research,
but also to demonstrate to young people, regardless
of socioeconomic backgrounds, that mathematics can
be fun and interesting to everyone.
Right: Professor Andrew Hazel demonstrating the mathematics
behind ribbon curling at the 2016 Big Bang Fair in
March 2016.
Answer to MathsBombe puzzle on previous page: 2044
Apprenticeships in Mathematics
Over the last two
years, the School of
Mathematics has
taken on an
apprentice from The
Skills Company. The
Skills Company offers
apprenticeships and traineeships across a wide range
of sectors to school leavers, young people and adults to
enhance their employability. This years’ apprentice,
Chloe-Alice Pike, tells about her time here in the
School.
I’m currently studying for my Level 2 Business Administration
NVQ, and have been placed at The University of Manchester
for my placement. The placement is one year long
and is spilt into two separate six-month placements. I began
my time at the University in The School of Mechanical,
Aerospace and Civil Engineering, and worked as an Academic
Support Assistant, before arriving here at the School of
Mathematics in March 2016.
I currently work as a PGR Admissions Assistant. On a
day-to-day basis my job responsibilities include processing
new PhD applications, liaising with applicants
and updating admissions records. I’ve found working
within admissions really interesting, as I enjoy reading
about the different kinds of applicants who apply to
study at the University, and finding out what has inspired
them to pursue Mathematics to this level.
Working at the School of Mathematics has taught me
so much. I work with a massive variety of people every
day, and I’ve learned that Mathematics isn’t actually
that scary!
The role has really helped me to focus on what kind of
career I would like to pursue once I’ve finished my
course. I work in the same office as the External
Relations team, and help out with careers and alumni
events. I really enjoy the organisation and
communication that goes into planning each event,
and I am definitely interested in developing my
knowledge and experience of this sector.
5

Taking a step back in time…
Elegant. Stylish. Incredibly ugly. These are just a few of the words used to describe the old Mathematics Building,
or ‘Maths Tower’ as it was informally known. Regardless of divided opinion, memories of this building
are vivid, nostalgic and often humorous within all minds that studied here. I went on a journey to find out
more about the iconic tower that soared above the Manchester skyline, and the incredible story (and people)
behind it...
Masterplans
The idea for the Maths Tower was first conceived as part of a wider post-war
vision for The Victoria University of Manchester. In 1949, the ‘Manchester
Plan’ was announced to reconfigure all Higher Education institutions into
some form of order. This idea for a wholesale reconstruction of the city was
similar to projects that took place after war devastation in London and Coventry.
Unfortunately the plan was never realised at this time. However, 20 years
later, in the 1960’s, a new push for change came in the form of the University’s
major building project, ‘The Manchester Education Precinct’. The project
involved a thorough (and visionary) plan to totally reinvent a number of key
institutions along the Oxford Road corridor, including The University of Manchester
Institute of Science and Technology (UMIST) on Sackville Street, various
colleges that merged to form Manchester Metropolitan University, and
The Victoria University of Manchester.
By Jenny Sloan
Above: The Maths Tower courtesy of Professor Nick
Higham.
The plan would also involve the creation of a new
commercial Precinct Centre, which would serve as
a busy commercial hub with shops, cafes and outdoor
dining areas.
An architectural trend at the time was to have elevated
walkways in the expressionist brutalist fashion
of the time. Architects of the Tower, Scherer
and Hicks, envisioned that the Maths Tower would
be well connected to the Precinct (as well as The
Royal College of Music and students’ Halls of Residence)
via these pathways.
Above: Artist’s impression of the Precinct Centre, with the Maths Tower looming
in the distance, as provided by Dr. James Hopkins, Heritage Manager at The
University of Manchester.
In reality, however, only two of these walkways
were actually built; one connecting the Precinct
Centre to the Royal College of Music, and another
leading to the main entrance of the Maths Tower.
Indeed, the remains of the latter can still be found
today, on the bridge of Crawford House, on Booth
Street East.
Left: One of the walkways , which ran through the Precinct Centre, that
connected the Maths Tower to the Kilburn Building.
6

Building of the Tower
The Maths Tower, built 1967-68, was the first building to be erected after ’The Manchester Education Precinct’ was
published. Standing at 18-storeys high on top of a three storey podium (which contained three lecture theatres and
several teaching spaces), the Maths Tower in fact still remains the tallest of all University buildings, past and present.
It was praised in architectural press as an ‘elegant’ construction of ‘grace and scale’ that was ‘optimistically conceived
and heroically realised’. The Tower was often illuminated at night, resting on the University skyline as a lighthouse
watching over the city. Indeed, its rather artistic albeit unusual architectural features, such as a triangular
staircase, were loved by many of its residents. It was even heralded by John Reade (a lecturer at the time) as a selling
point for ‘eager sixth formers’ who ‘gaped at the sixties chic and must have seen themselves in a James Bond movie’.
Both structurally and aesthetically, the praise for the Tower seems almost poetic;
The exterior is a bundle of cubic shapes, all of different heights, folding around each other, rising and dropping away,
seemingly at random. The slender verticality of the Tower has horizontal counterpoints.
Indeed, it was an architecturally great building, with its darkcoloured
brick forming a vivid juxtaposition with the glass and
light grey mosaic tiles. It housed over 450 undergraduates, 75
postgraduate and research students and 60 academic staff, all
within the Departments of Mathematics and the Mechanics
of Fluids. There were two lifts in the building that were built
to move at 350 feet per minute. The gross floor area of the
building was 102,775 square feet.
Above: A postcard from the 1970s illustrating the Maths Tower and
the Kilburn Building. Right: Photo of the Maths Tower taken by
Andrew Hamer on 29th June 1993.
The original plan was to surround the Tower with
grass, as a leafy oasis for weary academics.
Extra efforts were made by the architects to reduce
sound emission from bypassing traffic, including the
omission of windows in each of the three large lecture
theatres.
7

View from the Maths Tower, as photographed by Andrew Hamer on 29th June 1993.
Sculpture
The building was further embellished by a hollow concrete
sculpture made of geometrical spheres with hexagonal
holes in them. The sculpture was created by
the well-known Irish space sculptor Michael Yeomans,
and although it did not represent any mathematical
formula in particular, it was designed to capture an
essence of all mathematical formulae in a geometric
style. It was positioned on the south-west wall of the
building, overlooking a recreational patio.
The sculpture in 2015, courtesy of Professor Nick Higham.
Demolition
However, when the millennium brought the merging
of The Victoria University of Manchester and UMIST
under ‘Project Unity’ in 2001, the Maths Tower was
deemed unfit for use. There were many rumours to
why this was the case; some claimed it was accidently
built the wrong way round, others whispered
that it was in fact resting on a large underground
boulder which compromised its stability. One rumour
insisted that ‘every time the building began to
lean, calculations were done and heavy weights on
the roof were moved to keep the Tower standing, or
so the legend goes.’ Whatever the reason, demolition
was planned for 2005—its 36th year.
Phil Griffin, freelance writer and curator, pointed
out that while the building was not listed, it ‘is so
clearly a candidate for recycling, intelligent reprogramming
and skilful refurbishment’ and criticised
the University for ignoring its commitment to best
sustainable practice. He denounced the University
building for ‘totally lacking in style and imagination’.
Indeed, much of the Manchester community, and certainly the student body, were saddened to hear about its
impending demolition. Cyrus New (Mathematics and Philosophy, 2000) remembers, ‘I was sad to see it go… It was
ugly, but it was ours’. He remembers, ‘I was in Manchester with friends some years later and whilst driving down
Oxford Road in a taxi, I turned around to show them where I used to attend lectures, only to see thin air where it
once stood. It made me feel very old’.
8

Nevertheless, the demolition of the Tower was deemed necessary. The
new millennium marked an increased view of mathematics as a communal
activity, and just as scientists needed their laboratories, mathematicians
needed easily-accessible communal spaces for their own experiments.
This was not possible with a sixth floor common room, when the lifts were
unreliable and often breaking down, stopping academics and students
meeting up to converse about their work.
Indeed, the lecturers who worked in the Tower realised that this posed a
serious threat to the study and practice of mathematics, which now placed
greater emphasis on joint work. Nige Ray, a Professor of Pure Mathematics,
reminisces how Professor Michael Barratt, who has now sadly
passed away, led a team of lecturers who, when consulted at the time of
designing a new building, said ‘they didn’t mind as long as it wasn’t a
Tower ‘. It was paramount that the new building featured more accessible
communal areas. Nige pointed out that although he had ‘a big emotional
tie to the building and its view’ as he had spent ‘many of [his] formative
years in the Tower’, it was indeed ‘unfit for purpose’. He says that another
reason for its decaying relevance was that because it was built with concrete
it was very difficult to insert any IT infrastructure, an obstacle in our
age of modern technology.
Below: Both photographs documenting the demolition of the Maths Tower, as taken by Andrew Hamer on 29th June 1993.
University Place
The grave of the Maths Tower made way for the
new University Place building. Known as ‘The Tin
Can’, the £60 million project serves as a flagship
icon for the University. It is used as a general building
with 26 teaching rooms, two large lecture theatres
with a capacity for up to 1000 people, as well
as acting as a home to a gift shop, café, canteen
and the University’s Visitor Centre.
Left: aerial view of the Oxford Road Corridor, featuring Whitworth Hall, with
the Maths Tower opposite it, and the Roscoe and Ellen Wilkinson buildings.
9

The Alan Turing Building
The School of Mathematics was formed during the merging
of The University of Manchester Institute of Science and
Technology (UMIST) and The Victoria University of Manchester.
The pay-off for some of the School spending a few
years with their offices in ‘insulated sheds’, was the modern
Alan Turing Building.
Indeed, now the School of Mathematics has moved only a
few hundred metres away from where the Maths tower
once loomed. After four years of design and constructions,
the Alan Turing Building opened its doors in 2007. Designed
by Sheppard Robson, the £43 million building was shortlisted
for the Greater Manchester Building of the Year 2008,
organised by the Greater Manchester Chamber of Commerce.
The building consists of several classrooms named after
famous mathematics Louis J. Mordell, Lewis Fry Richardson,
Max Newman and James Lighthill. Additionally, it contains
computer suites, seminar rooms and meeting rooms named
after Brian Hartley, Sydney Goldstein, Frank Adams and
Horace Lamb.
There is now plenty of communal spaces for staff and students,
undergraduate common rooms, shared computer
suites, work rooms and quiet study rooms, as well as the Pi
in the Sky Café.
The most popular meeting place in the building is the communal
area on the Atrium Bridge, where academic staff and
students gather for coffee every morning (below middle).
10

Your Maths Tower Memories
I was at Manchester 1982-85. Before I arrived, there was
a lovely photo of the Maths Tower on a postcard,
bathed in the sunshine—only actually being in Manchester
did I discover that clear skies were limited to freezing
cold winter days! - Mick Morris
There was a rumour that Nige Ray thought
the room allocated to him on the plans
was too small, so he befriended the builders
and persuaded them to make it bigger!
- Richard Sharp
When we moved into the Tower the segregation
was remarkable; second and third years in the Max
Neuman room playing bridge, first years in the library
studying. Room 105 was the committee room
for the Maths Colloquium (luxury), with its own telephone
(absolutely luxury!).—Chris Reynolds
My most vivid memory is being in the
Tower on the second floor when the
3.9 TS earthquake struck on 21st October
2002 at 12.42pm. I was in the
Linux Cluster in the middle of a CFD
class when the building shook. The
lecturer (clearly disturbed by the
event) just got up and left straight
away without a word! We all looked
at each other and figured it was time
to pack up our things and leave. When
we left we found huge numbers of
people gathered in the foyer. One of
my friends had been in her office on
the 16th floor at the time and she said
that she felt the whole building sway
from side to side.—Leena Murgai
The toilet paper was pink and highly
abrasive… that was a memory that has
been hard to shake off! - Cyrus New
Hmmm… what I remember about the Maths
Tower? Paper recycling! - Michael Bane
The tower itself offered a great view of the
nearby mountains. I remember one time, I
had 24 hours to finish a pile of marking
and did an all-nighter in my office, which
was on the ninth floor with windows in
three directions. The whole time I was
sitting at my desk I saw the sun going
down, the party goers, the sunrise and the
midday sun. And another time, I remember,
on the 16th floor you could actually
feel a light oscillation when the wind was
blowing hard.—Sara Santos
I remember it was possible to get to the outside
of the tower as there was a balcony just
outside the ladies toilets on the 17th floor. It
was a nice view of the hills once you climbed
through the window.—Chris Cowan
The porter sending up bottles
of milk in the lift! - David Brown
There was a legend that the Maths
Tower had been built the wrong
way round… -Martin Waters
11

And finally, to put those rumours to rest...
As my Maths Tower journey came to a close, I felt it was necessary to talk to Professor Nige Ray, who was the Head
of Department during the last years of the Tower’s life. As soon as I sat down with Nige over a coffee on a drizzly
Tuesday morning in the Pi in the Sky café, I had to ask him about a number of rumours flying around about himself
and the Maths Tower.
‘Is it true that you missed the earthquake in October 2002, because you were in the toilets?’
(There was a shallow earthquake swarm beneath Manchester city centre, which
lasted about three months. In fact, in total there were 150 tremors, the largest of which
was ML4. A total of 30 were actually felt, although they only caused some minor damage.)
Nige laughed at my question, ‘Absolutely not! I was in my office on the 11th floor,
when I heard a tremendous booming noise before the whole building shook, wavering
backwards and forwards’.
Nige immediately recalled the earthquake training he had received while living in America, and rushed to position himself
under a door frame while his colleagues looked at him in bewilderment. He remembers his colleague, Douglas Gregory
(who has now retired) delivering a lecture at the bottom of the building when the earthquake took place,
‘Apparently the whole theatre was stunned, and there was total silence for about five seconds after it ended, before a
student in the back row shouted “Douglas, do it again!”.
The next question I had was one that many alumni have contacted me about, the stories of the Maths Tower being built
backwards. ‘No, definitely not’, Nige laughs, ‘While the Tower did turn out to be very different from the original plans, it
was built the right way round!’. I was pleased that the safety of the Tower was verified, considering the Tower housed
thousands of students and staff throughout its lifetime. But how different did the Tower actually turn out to be? Nige
revealed that the original plan was to close Oxford Road entirely and reinvent it as a pedestrian- and bus-only zone (a
plan that has been resurrected in recent months). ‘The architects wanted the main entrance of the building to be located
on Oxford Road’, Nige explains, ‘however, when Oxford Road remained open to traffic they had to squash the building
back a little’.
However, before Nige went back to teaching and I to the office to polish off this article (!), I had one final question… ‘Is it
true you befriended the builders and convinced them to change the plans to make your office bigger?’ I laughed. This
warranted a knowing smile, and after a short pause, Nige chuckled, ‘Well yes, that one is true! I bought them a bottle of
whiskey in exchange for them moving one of my office walls back nine inches or so. It meant I could fit my bike in the
office comfortably’.
The 2016 Careers in Statistics Fair
On 2nd March 2016, the School of Mathematics hosted the
annual Careers in Statistics Fair. Supported by the Royal
Statistical Society Manchester Local group, the event acted
as a networking opportunity for students who are considering,
or about to embark on, a statistical career.
Nathan Prabhu-Naik, from the HMRC, talking to MSc students.
The event began with students browsing employer stands
and ended with a series of employer presentations covering
fields as diverse as medicine, finance, industry, environment,
government and academia. Among the speakers were
representatives from the HMRC, Royal Statistical Society,
Lubrizol, AstraZeneca, Ernst and Young and Medical Statistics
in Academia. The event was a great experience for all
attendees, with nearly 100 students in total registered.
12

The Padlock Icon and a Million Dollar Maths Problem
By Dr. Carolyn Dean
When we make an online purchase
with a credit or debit card
it is a good habit to check for the
padlock icon, which indicates that
we can transmit our private data
securely. But what does this really
mean?
The padlock icon indicates that
our data is being transmitted in an
encrypted form. Encrypted information
travels over the usual
channels, but it is disguised so that an eavesdropper cannot
read it.
The most widely used encryption system for e-commerce
was invented by Ronald Rivest, Adi Shamir and Leonard
Adleman at MIT in 1977 and is called RSA. Its power
derives from properties of factorising integers dating back
to the ancient Greeks.
Left to right: Adi Shamir, Ronald Rivest and Leonard Adleman
As we will see below, this power source is either a great
thing or a potentially fatal weakness, and to this day no
one knows which it is. Furthermore, this question is
closely related to one of the seven Millennium Problems
chosen by Clay Mathematics Institute. Each of the Millennium
Problems carries a prize of one million dollars.
If you wish to receive securely transmitted credit card
details encrypted with RSA you begin as follows. Recalling
that a positive integer p is prime if p > 1 and the only
divisors of p are 1 and p, you pick two prime numbers p
and q and form n = pq. You also form the number
t=(p-1)(q-1).
Using t and some important work of the 18 th century mathematician
Leonhard Euler, you choose a companion number
e and broadcast the public key (n, e). You also use t to
compute a number d that is a partner to e.
The number d is your private key.
Crucially, p, q, t and d must be
kept secret.
We use RSA in the following manner.
Let us suppose that I wish to
send you my card details, and let
M denote my card number. We
require that M < n and that neither
p nor q divide M; in practice
this is easy to arrange. I encrypt
my card number by taking M e and
use only the remainder upon division by n. We will call this
number R. When you receive R (over an open channel)
you take R d . By using the partnership between e and d and
working with remainders, you alone are able to recover M.
Throughout this process you and I have never shared a secret.
Thus RSA is an example of public key encryption, a
late 20 th century paradigm shift in the field of cryptography.
If n is factorised it is easy to find t, d and my card number.
A quick method for factorising large numbers would sound
the death knell for RSA. Current guidance suggests that
when n has 2,048 bits or 617 digits and p, q have about
300 digits each, the factorisation of n can resist attack for
10 to 15 years. A 4096 bit key n should be safe for the
foreseeable future. (All of this may be invalidated by advances
in quantum computing.)
This guidance is based on our current factorisation algorithms,
which have not come very far in 2,400 years. We
tend to think that because we haven’t found a fast factorisation
algorithm in all this time no such algorithm exists.
However, proving a negative of this nature is a very difficult
problem. The upshot is that no one really knows how
secure the most widely used e-commerce cryptosystem in
the world is.
Factorisation is an interesting question because it is easy to
verify a given factorisation; finding the factorisation in the
first place is a much harder problem. Given the number
n=194,947, told that n is the product of two prime numbers
and directed to factorise n using only pencil and paper,
most of us would experience a certain sinking feeling.
In theory the task is not difficult but in practice it is a first
class nuisance. On the other hand, when told that
383 x 509 = 194, 947
we can verify this statement quite easily. The contrast in
these exercises scales up to calculations performed by a
computer.
The Millennium Problem P vs NP concerns this dichotomy.
Roughly speaking, P denotes the class of problems that can
be solved on a computer `easily’, with algorithms known as
13

polynomial time algorithms. Determining whether a number
is prime and calculating the greatest common factor of
two numbers are examples of problems in P. The class NP is
more subtle: NP means nondeterministic polynomial time
and the definition requires that true instances of problems
in NP must be verifiable in polynomial time, or `easily’. Every
problem in P is in NP and, as our example suggests, factorisation
is in NP.
The Millennium Problem P vs NP asks whether P=NP. If
every true instance of a problem can be verified easily, does
the problem itself admit an easy (polynomial time) algorithm?
Factorisation is just one of many problems in NP of
which this question can be asked.
Credit for conceptualising public key encryption in 1974 is
assigned to Ralph Merkle, then a postgraduate student at
Stanford University, and credit for its first implementation
goes to Merkle’s doctoral supervisor Martin Hellman and his
colleague Whitfield Diffie, who published their result in
1976. Again, though, GCHQ had got there first. In 1969
James Ellis had developed the concept of public key encryption,
and in 1974 Ellis’s colleague Malcolm Williamson implemented
the protocol known as Diffie-Hellman Key Exchange.
By the 1980’s there was little point in maintaining the classified
status of the work done at GCHQ. Decisions on declassification
don’t come quickly. On 18th December 1997
Clifford Cocks gave a conference presentation on the history
of public key cryptography research at GCHQ, revealing the
seminal contributions of Cocks, Ellis and Williamson to their
peers and to the world. A month earlier, on 25th November
1997 James Ellis had died.
If an easy factorisation algorithm is found then RSA becomes
useless, factorisation is in P and P vs NP remains
open. If it is proved that no easy factorisation algorithm
exists then the fundamental security issue for RSA is
settled, factorisation is not in P, and P vs NP becomes only
the second of the seven Millennium Problems highlighted
by the Clay Foundation 16 years ago to be solved.
Left to right: James Ellis, Malcolm Williamson and Clifford Cocks
The history of RSA and public key encryption is less well
known than it should be. The RSA cryptosystem was first
invented at GCHQ in 1973 by Clifford Cocks; because it was
classified, the world knew nothing of it.
Left to right: Ralph Merkle, Whitfield Diffie and Martin Hellman
Better World Award Winner 2016
The School of Mathematics celebrates a win at The Better
World Awards 2016.
The Better World Awards are the Faculty's first awards to celebrate
and recognise excellent work and activities relating to Social Responsibility.
On 8th February 2016, Helen Harper, Sebastian
Rees, Charles Walkden, Andrew Hazel and Kees van Schaik were
awarded the 'Outstanding Public Engagement Activity Award',
which recognises and celebrates the work of staff who engage with
the public to share knowledge and/or enrich lives.
The award was in recognition for their hard work and excellent
effort working on The Alan Turing Cryptography Competition
(more details of which can be found on page 4).
14

Interview with an Alumnus
By Jenny Sloan
On a rainy, sub-zero afternoon in the Alan Turing building,
I had the pleasure of meeting and interviewing one of our
Mathematics Alumni, Rohana Gunawardena. Rohana began
his BSc Mathematics at The University of Manchester
in October 1984, and has since developed an impressive
career with some big names encompassing a vast geographical
arena.
Unlike many alumni (including myself), Rohana had a very
clear idea about what he wanted to do after his graduation
in 1987. He explains that after university he started working
‘in the consulting division at PwC, which was then called
Deloitte’. He worked as an Auditor for three years, before
moving on to Consultancy
within the same organisation.
This then led him to
another role in Consulting,
‘with Accenture, which was
then called Anderson Consulting’.
A clear interest and flair for
consulting can be tracked
from Rohana’s early graduate
career, so it may not be
surprising that he decided
to start up his own company, Exium Inc, ‘specialising in
providing high quality consultants for long term assignments’.
However, one of the main things that working as a
Principal Consultant within his own organisation taught him
was that one can ‘achieve more working with other people’.
Between 1997 and 2007, he worked with ‘several
different clients’, from Applied Materials to GTECH.
Indeed, in the Autumn of 2000, Rohana began working for
Applied Materials, and stayed with the company for more
than fifteen years. He worked on a project revolving around
‘SAP, which is a brand of German software’, and was
‘initially hired to work on SAP roll-out to Japan’. However,
the project ended up taking him to the USA, where he carried
out ‘consulting work on the East Coast’ for five years.
And the rest, as they say, is history. Rohana has been in
Northern California ever since, and has been working as
Director of SAP Practice with Quality Systems & Software
(‘a Business & Technology consulting firm with a special
focus on maximising EPR investment’) since June 2007.
While at university, Rohana was taught by lecturers such as
Peter Eccles and Francis Coghlan (pictured below, with Nige
Ray), and remembers his time at the University fondly. Besides
working for The Mancunion as a photographer and
enjoying membership of the squash team, he found his degree
to be stimulating and it allowed him to gain excellent
knowledge and skills. Rohana reveals that the day to day
principles and practices of Mathematics are not relevant
every day in his role. He laughs, ‘I’m not faced with algebra
or vectors on a daily basis’.
However, his degree is still pertinent in his current role,
primarily the ‘problemsolving’
he developed
throughout his degree. His
time studying Mathematics
at The University of Manchester
taught him to ‘not
be phased when [he] see[s]
something difficult’, and to
‘not be scared of Maths’ in
it’s shapeshifting forms,
which is, in Rohana’s case,
software. Indeed, he encourages
current Mathematics
students and alumni to be proud of what their
Mathematics degree has given or is giving them. ‘I would
expect anyone studying Mathematics to have strong technical,
mathematical and computing skills’ he explains, however
‘it’s the soft skills that they may need to work on’. Indeed,
these ‘soft skills’ have proved to be most beneficial
for advancing Rohana’s own career. He advises
‘communicating and understanding business problems
from the perspective of a business user’ are crucial for success.
Now based in the San Francisco Bay Area, Rohana’s interests
include ‘barbeque [which] is the major summer activity
now that [he] is a home owner’ and ‘sampling the best the
Bay Area has to offer’. He has also been the University’s
main contact for Northern Californian alumni for the past
five years, having helped to deliver ‘International Speaker
Series’ events in the San Francisco area. These involve a
particular academic investing a few hours one evening to
meet with alumni to deliver a presentation on their particular
area of research, while also distributing headline
15

information about The University of Manchester. Rohana
has been instrumental in helping the Division of Development
and Alumni Relations pilot this programme, which
has featured three events over the past six months.
Rohana explains that he plays an active role in encouraging
networking opportunities for alumni because he himself
enjoys meeting new people and connecting via their
‘shared experiences’ of studying at the University. A
memory that springs to mind is ‘going to The Plaza Curry
House’ (which used to be on Upper Brook Street, and I’m
told it was a hive for young students fuelled by competition
over who could eat the hottest curry). Other memories include
nurturing relationships with academic staff and classmates
and attending several ‘events in the Students’
Union’.
When I asked what kind of alumni he shared these experiences
with in the Northern Californian group, Rohana
revealed that he does not know many Mathematics alumni
in the Bay area, but has connected with quite a few from
the Alliance Manchester Business School and the School of
Computer Science, which is ‘understandable with the Silicon
Valley so close’. Additionally, Rohana also welcomes
current Manchester students to his workplace once a year
through the Global Graduates Programme.
While he clearly loves the West Coast way of life, and is
extremely passionate about his role, he shows some nostalgia
for the UK, admitting ‘the television is much better [in
the UK], with the BBC…and the newspapers are much
better!’ He also explains that he ‘misses friends from [his]
school, neighbourhood and university’. This last admission
reminded me of the importance of our alumni community,
which succeeds through nurturing existing relationships,
reviving past friendships and connecting with future friends
and opportunities.
New Research Grants
Prof. Nico Gray has been awarded an EPSRC Established Career Fellowship worth £1.4M. Entitled
‘Particle-segregation in Chutes, Silos, Conveyor Belts and Rotating Drums’, the primary
objective of the fellowship is to develop a fundamental quantitative understanding of particle
segregation in industrial flows.
Prof. Jack Dongarra is PI on an EU grant, ‘NLAFET’. The award is for £658,436, and the project
aims to enable a radical improvement in the performance and scalability of a wide range of
real-world applications relying on linear algebra software, by developing novel architectureaware
algorithms and software libraries, and the supporting runtime capabilities to achieve
scalable performance and resilience on heterogeneous architectures.
Dr Gareth Jones has been awarded £337,789 by EPSRC for a standard grant entitled: ‘Model
Theory, Functional Transcendence and Diophantine Geometry’. This is a joint project with Jonathan
Pila in Oxford, and will continue their recent research into the interaction between model
theory and diophantine geometry, and prove further instances of the Zilber-Pink conjecture.
Along the way they hope to also prove new functional transcendence results using methods
from model theory.
Dr Raphael Assier has been awarded £93,588 for his EPSRC First Grant: ‘Canonical Scattering
Problems’. The project will focus on two important canonical problems for the mathematical
theory of diffraction: wave diffraction by a quarter-plane, and wave diffraction by a transparent
wedge. The first problem is related to the understanding of noise production by blade-gust interaction
in aeroengine or underwater propulsors, while the second is related to the understanding
of light diffraction by ice crystals contained in clouds, an important factor to take into
consideration in climate models.
16

Jack Williams (1943-2015)
Jack Williams sadly passed away on 13th November 2015,
at the age of 72. After obtaining his PhD in 1968 from The
University of Oxford Computing Laboratory,
Jack spent two years working as a
Lecturer in Mathematics at The University
of Western Australia in Perth. In
1971, he was appointed Lecturer in Numerical
Analysis here at The University
of Manchester.
Jack’s main research area was approximation
theory, focusing particularly on
Chebyshev approximation of real and
complex functions. He also worked on
stiff ordinary differential equations
(ODEs). His early work on Chebyshev approximation in the
complex plane by polynomials and rationals was particularly
influential and is among his most-cited.
By Nick Higham
It’s a fact of academic life that seminars can be boring and
even impenetrable. Jack could always be relied on to ask
insightful questions, whatever the topic, thereby improving
the experience for everyone in the room. Jack was an excellent
lecturer, who taught at all levels from first year undergraduate
through to Masters courses. He was confident,
polished, and entertaining, and always took care to emphasize
practicalities along with the theory. He had the
charisma—and the loud voice!—to keep
the attention of any audience, no matter
how large it might be.
Jack was promoted to Senior Lecturer in
1996 and took early retirement in 2000.
He continued teaching in the department
right up until the end of the 2014/2015
academic year. I benefited greatly from
Jack’s advice and support both as a postgraduate
student and when I began as a
lecturer. My office was next to his, and
from time to time I would hear strains of
classical guitar, which he studied seriously and sometimes
practiced during the day. For many years I shared pots of
tea with him in the Senior Common Room at the refectory,
where a group of mathematics colleagues met for
lunchtime discussions. Jack was gregarious, ever cheerful,
and a good friend to many of his colleagues. He will be sadly
missed.
This article has been shortened for clarity. Originally published:
https://nickhigham.wordpress.com/2015/11/30/jack-williams-1943-2015/
Eric J. Watson (1924-2015)
Eric Watson was an extremely humble man with great mathematical
prowess, and he enjoyed a varied professional career.
After graduating from The University of Cambridge, Eric
worked at the National Physical Laboratory and Liverpool
University. He went on to found the Institute of Mathematical
and its Applications, acting as the President of the North-
West Branch for some time. In 2014, Eric was awarded a
certificate recognising his 50 years of membership from
Dame Celia Hoyles during the Institute’s 50 th anniversary
celebrations.
In the 1950’s, Eric was appointed Lecturer at The University
of Manchester. Eric possessed formidable mathematical
skills. For example, during a seminar at The University of
Manchester, Eric masterfully identified a numerical computation
of a complex algebraic expression to be the eighth
Bernoulli number!
In his free time, Eric enjoyed hill walking, and was also an
active member of Didsbury United Reformed Church. Although
he retired early in 1982, Eric remained very mathematically
active until recently and often attended the
Wednesday afternoon seminars held by Mathematics Today.
Personal recollections of Peter Duck, Head of School, The
University of Manchester
I first met Eric when I was interviewed for a lectureship in
Manchester. Although Eric was not a prolific publisher of his
researches, I had the pleasure of being a co-author of one of
his papers. The Appendix to this paper contains a classic
piece of ‘Watsonese’, where the solution of ab ordinary
differential equation is written first in terms of confluent
17

hypergeometric functions, and then in terms of gamma
function together with an infinite sum of zeta functions. I
feel greatly privileged to have known such a modest man
with great mathematical prowess.
privileged to have known such a generous and kind-hearted
individual, who helped me significantly early on in my
career.
Personal recollections of David Abrahams, Beyer Professor
of Applied Mathematics, The University of Manchester
I first met Eric in summer 1982 when I took up my first lecturing
position (at Manchester). I was just bringing in my
boxes of work to the (now demolished) Mathematics Tower
when Eric wheeled out his bicycle on which was strapped a
huge pile of his research papers and books. He was just
clearing his room to ‘downsize’ for his move to a retirement
office. He wobbled away with the ungainly load behind him,
and at the time I did worry for his safety on his journey
home to West Didsbury!
Fortunately, Eric did not treat formal retirement as a reason
to change his research behaviour, so he was a very regular
visitor in the School of Mathematics until very recently. I was
Eric Watson receiving a certificate for 50 years’ membership of the IMA
from Dame Celia Hoyles
This article has been shortened for clarity but originally appeared in the
February edition of Mathematics Today (1 Feb 2016, Vol. 52, No. 1)
Michael McCrudden (1943-2015)
Dr Michael ‘Mick’ McCrudden began his Lectureship
in the School of Mathematics at Manchester in 1971,
and remained at the University until his retirement in
2010. During this time, he held the positions of Senior
Lecturer and Reader.
the Mathematics Tower). He enjoyed five-a-side
football with staff and students of the Mathematics
Department, and was an avid singer, songwriter and
guitarist who loved to entertain all. He will be sadly
Mick was born and lived in Derry, Northern Ireland
for most of his youth, graduating from Queen’s University
Belfast with a BSc and MSc in 1964 and 1965
respectively. He enjoyed a full and interesting career,
allowing him to travel to many places across the
world.
Mick was a popular lecturer at the University, teaching
and inspiring students of all levels, from first year
undergraduates to those at Masters level. His brilliant
sense of humour brightened up even the most
routine of lectures.
Indeed, Mick himself was a gregarious, jovial man,
who loved to socialise with his colleagues at the University,
both during lunch and in the evenings, when
many would flock to the College Hotel (and later to
18

All aboard for Mathematics!
Alumnus interview by Jenny Sloan
Many people assume our Mathematics alumni pursue
careers in accountancy, finance, IT or teaching. However,
there are many who travel off the beaten track.
Having graduated in 2000, Neil Horrocks, dismissed the
mathematician stereotype and followed a very different
path. Neil now works as a cruise Director and Expedition
Leader for a cruise liner. I caught up with him to
find out more about his journey into the entertainment
and hospitality world, the challenges
and wonders of this industry,
and how Mathematics at
Manchester helped him to progress
within his chosen field...
Hi Neil, thanks for agreeing to
share your incredible and intriguing
journey with us. Currently
you’re in Japan, then flying directly
to another cruise liner in Iceland,
before spending a week in
New York. Your current situation
is (literally) a thousand miles away
from Manchester. What made you
come to The University of Manchester
to study?
Yes, it’s all go here at the moment!
I chose to go to Manchester for a
variety of reasons. I can still remember
my UCAS options. I was offered places at all of
them, but it was Professor Fred Loebinger, of the Physics
department, who interviewed me for Manchester. He made
me feel wanted and was very enthusiastic about the University
and the city. I was also tempted by the chance to watch
some Manchester City games, although my four years coincided
with their worse form in living memory! And finally,
the summer before I went to Manchester, ‘Oasis’ had
played at Maine Road and it felt as though Manchester was
the centre of the cultural universe at the time. It was definitely
the right decision, I had a fantastic four years in the
most vibrant of cities and I’m proud to be an alumnus.
We would definitely agree The University of Manchester is
the place to be! What made you want to study Mathematics
here?
Neil on the beach at Jost Van Dyke in the British
Virgin Islands
I originally started off doing a joint degree in Maths and
Physics, but transferred to pure Maths half way through.
When I was at Worthing Sixth Form College, I had an excellent
Pure Maths teacher called Roger Quittenton, who inspired
me to take the subject to university level.
I definitely think it’s true that passion for STEM begins at
school, that’s why the School works so hard on our outreach
programmes. Since graduating, you’ve made a name
for yourself within the hospitality
and entertainment industry. Was
this your plan throughout university?
No, certainly not. In fact, I actually
spent a year working in the financial
sector after graduation. However,
whilst I always enjoyed Maths, I’ve
always been of the belief that university
is a time to get involved in a wide
variety of activities. Again, it was Roger
Quittenton (who was an international
rugby refugee) who told me
before I sat my A-Levels that we all
gain different things from university
life, but each experience is just as
important as the other. And I tried to
get involved in as many extracurricular
activities as possible alongside
my Mathematics degree. I became
Senior Student at Dalton-Ellis
Hall and I was Musical Director for the Drama Society. I remember
Roger advising me that some students continue to
excel within their chosen field, whilst others develop skills
of which they weren’t even aware! I guess the latter is what
happened to me, because if you had told me I would end up
spending my life sailing around the world I would never
have believed it!
After my graduation in 2000, I worked full time at Lloyds
TSB share registry in Worthing. The role was mostly dealing
with the administration of share transactions, and whilst I
didn’t personally feel very enthused by it, it was a good discipline
and paid off my student overdraft. At that time, I
found myself applying for transport companies as a role in
logistics and customer service appealed to me. However,
after only a year in the financial sector things took a
dramatic turn…
19

And this marks your transition into the dazzling entertainment
sector on luxury cruise liners! What inspired this dramatic
change?
We had a lot of temporary staff at
the share registry, and one of
them was reading the variety
newspaper “The Stage” at
lunchtime. Once they’d finished
with it, with nothing of my own to
read, I asked if I could have a look
at it. I saw a job advertised asking
for “Cruise Staff” with Fred Olsen
Cruise Lines. The job description
sounded quite appealing and I’d
never travelled abroad other than
the occasional day trip to France and Belgium and a week
on the Isle of Wight. I edited my CV to put greater emphasis
on the extra-curricular activities I’d been involved with at
university in the hope that the interviewer would take a
chance on me. Sure enough, they commented that they’d
never had someone with a Pure Mathematics degree apply
to be cruise staff on one of their ships. I replied that at least
I’d be qualified to do the bingo, and with that I was offered
the job!
This proves that a degree in mathematics can open up so
many different doors! You then worked your way up the
career ladder to become a Cruise Director and Expedition
Leader. How did you find this progression? Did you face
any hurdles along the way?
Meeting a local in Uwajima, Japan
The ‘Spirit of Adventure’ went everywhere. We went as far
north as the Arctic, as far south as Antarctica, as far west as
Acapulco, and as far east as New Zealand
– although every year we’d return
to the UK for the summer season.
Now I work as a Cruise Director for
Noble Caledonia. This role was definitely
a new challenge for me, as the
ships only carry a maximum of 100
passengers, and are of such size that
they can reach the remotest and
smallest of harbours. However, if a
harbour is not available then we have
a fleet of inflatable crafts (called
‘zodiacs’) and can operate a beach landing. It truly is expedition
cruising and I love how every day is a new challenge.
There was quite a lot of suspicion towards me at first, given
my unconventional route into the cruise industry, but I soon
realised that there was potential to rise up the ladder. I
watched my colleagues and learned from what they did well
and not so well. I rose up the ranks at Fred Olsen, becoming
Senior Cruise Staff and then Assistant Cruise Director. However,
I fancied trying my hand at one of the large cruise
ships that you see in the major ports, so in 2004 I joined Celebrity
Cruises then-flagship “Constellation”. I can recall being
up on deck at 5am to watch us sail into New York harbour
on my first visit to that incredible city – definitely the
best way to arrive!
After six months with Celebrity I joined Saga Cruises and
spent over eight years there. It was during that time that
Saga launched a ship called “Spirit of Adventure”. The idea
behind these new liners was that passengers could fly out to
join the ship wherever it is in the world. This was where I
truly thrived and I became Cruise Director at the age of 27,
which is very young for this industry.
Neil standing on a zodiac watching the sunset at San Juan Del Sur, Nicaragua
That sounds fascinating! I’m getting serious wanderlust
hearing about your job. Where was your favourite place to
visit?
Gosh, it’s so hard to say! I have visited 147 countries since I
started cruising 15 years ago. Some places are now tinged
with sadness in that, at the time, I didn’t think that I would
not be able to go back. For example, the visits to Libya, Syria,
Lebanon, Yemen, the Crimea – never did I think that the
incredible historic sites there would become off-limits.
Most recently, I enjoyed visiting Livingston in Guatemala.
We took a small boat up a river to an extensive project
where local Mayan children from the riverside villages can
stay and receive a good education. It is a privilege to visit
places like that where a real positive difference is being
made to peoples’ lives. I was also able to offer a donation
from the Noble Caledonia Charitable Trust as part of our
20

ongoing efforts to ensure that we put as much into the local
development of places we visit as possible.
Currently I’m in Japan and I don’t think I have ever met a
kinder, friendlier or more generous people than the Japanese.
Every port we visit has some form of welcome committee
on the quayside offering complimentary gifts to the
passengers, and then local school children often appear on
the quayside as we are preparing to leave and perform fantastic
routines. Their generosity of spirit is incredible.
many different walks of life. One particular standout
memory was taking part in an on board version of “Can’t
Cook, Won’t Cook” with celebrity chef Kevin Woodford. He
was hosting the event whilst I had to compete against the
formidable Betty Boothroyd. Having been in catered halls
for four years and then working at sea my cooking skills are
non-existent, but I think the result was still a diplomatic
draw!
I also love taking the ship to places that are rarely visited,
and seeing the reaction of the locals! One time we sailed up
the Amazon River, and all the locals rowed out to the ship in
their dug-out canoes. Another time we took a steam train in
Eritrea and the local children ran alongside the train waving
at us. So many wonderful memories!
Standing on top of a Mayan monument in Lamanai, Belize
You’ve described some pretty amazing experiences, but
what do you do on a day-to-day basis onboard?
Neil with former Speaker of the House of Commons, Baroness Betty Boothroyd
The beauty of my role is that there is no ‘typical’ day. While
there are always some tasks that need to be done (like
writing the next day’s programme etc.), no two days are the
same. Some days will involve simply arriving in a port and
heading off on a shore excursion in a coach, whilst others
might involve a beach landing on an uninhabited island. Occasionally
we’ll have a day at sea where I look after the lecture
and entertainment programme. I am also constantly
negotiating with the Hotel Manager and Captain about the
way the cruise is progressing. Recently, whilst out in the
Caribbean, we had to cancel three ports in a row due to a
passing storm, so I found myself standing on the Bridge and
using the satellite phone to call other islands with sheltered
harbours asking permission to go there instead. It’s certainly
never a dull moment on board!
You certainly must have a very expansive job description!
What is your favourite part of the role?
The genuine satisfaction at the end of a cruise, knowing that
my passengers have had a thoroughly enjoyable time with
us. I meet so many different characters over dinner, from so
This sounds too good to be true! Surely you have bad days
like the rest of us?
Of course. Arguably the worst day I’ve had on board was
when we were attacked by Somali pirates in early 2011 enroute
from Mayotte to Zanzibar. Fortunately they didn’t get
aboard and we had been drilled in the relevant procedures.
At the time it was happening we just got on with the task in
hand, but the next day there was an element of shock as we
thought about what might have been.
Sounds terrifying! Has your Mathematics degree aided
your career progression in this industry (or helped you
cope with the pressures of the role)?
In a nutshell, YES. One of the areas of Pure Mathematics
that I particularly enjoyed was propositional logic, and I feel
that had a strong positive influence on me in my current
role. I am able to bring clarity of thought and logical approach
to the most awkward of situations – be it a flight
delay meaning we will have to hold the ship and then
change the timings and/or itinerary for the upcoming ports,
21

or sea conditions causing us to divert our course. As long as
you are honest and clear with the passengers about why you
are taking such actions and how things will be affected then
they will always be on your side. I dine with the passengers
every evening and many presume I studied Travel and Tourism
or Geography at University to have ended up in this line
of work, and are stunned to discover I read Pure Mathematics
at Manchester. It certainly is an excellent conversation
starter!
My advice would be to do it while you can! I made the
change just a year after graduating, and haven’t looked
back. The beauty of having a degree from The University of
Manchester is that it is internationally recognised as a magnificent
seat of learning, and once you have that degree, noone
can take it away from you. You can always fall back on it
and use it elsewhere. When I started working on cruise ships
I had no idea whether or not I would last 15 minutes, let
alone 15 years. However, I did it knowing that if it didn’t
work out I could hold my head up high, knowing I’d given it a
try, but then use my honours degree to gain employment
elsewhere. You never know what doors will open in front of
you or where your path will lead, but it was the best decision
I ever made. I very much doubt I would have made the
change without having the experience of life at a world-class
university and the strength of character and determination
to succeed that was bestowed upon me.
Playing with a Cuban band in Havana
Have you ever met any Manchester alumni while chatting
with your guests?
Yes, over the course of dinner conversations I have often
come across fellow Manchester alumni. Many are interested
to talk about the merger with UMIST, and about how they
remember the university. It seems strange to think that I can
add to those memories now, given the changes that have
taken place in the relatively short time since I graduated.
The Maths Tower doesn’t even exist anymore. I just wish I’d
taken a photo from the 17 th floor when I had my tutorials
with Dr Alan Jones! What I find fascinating with talking to
fellow alumni is how not only they speak about how the university
has developed, but also about how the city itself has
developed. Manchester is certainly ever-changing and it’s
always interesting to go back there and discover areas that
have had a new lease of life. The city has an incredible personality
which I feel is both partly driven by and reflected in
the vibrancy of the University.
Sailing under Sydney Harbour Bridge, Australia
Standing on the monument of Borobudur on the Indonesian island of Java
What advice would you give other Manchester alumni who
are considering a career change?
On the back deck sailing down Milford Sound in the New Zealand fjords
22

Dame Kathleen Ollerenshaw Lecture 2015
By Helen Harper
The 2015 Dame Kathleen Ollerenshaw Lecture took place
on Thursday 8 October 2015. The annual lecture is named
in honour of Dame Kathleen Ollerenshaw, who sadly
passed away last year aged 101.
Born in Manchester, Dame Kathleen is best known in mathematics
for her work on magic squares but she had many
other interests including astronomy and politics. She
worked tirelessly to promote mathematics, particularly
amongst young people and was a strong supporter of
mathematics in Manchester (she held honorary degrees
from both The University of Manchester and UMIST). Coping
with deafness from the age of eight she was an inspiring
role model to many.
This year’s lecture was given by Professor Marcus du Sautoy
who, like Dame Kathleen Ollerenshaw, has done much
to popularise mathematics. Marcus is a Professor of Mathematics
at The University of Oxford, and is also the Simonyi
Professor for the Public Understanding of Science. In 2010
he was awarded the OBE “for Services to Science” and has
written several books of which the most famous is The Music
of Primes.
Professor du Sautoy’s lecture, entitled “The Secret Mathematicians”
explored how mathematics can be found in nature.
He pointed out that it is unlikely that the 17-year lifecycle
of the insect cicada is coincidence but rather has
evolved to avoid the life-cycle of some kind of predator.
Marcus du Sautoy
also named a number
of “secret mathematicians”;
people
whose work in the
field of arts can be
shown to be underpinned
by mathematical
ideas. At
one stage the audience
listened to a
piece of music by
the French composer
Oliver Messian,
which was built by rhythmic and harmonic sequences structured
around the prime numbers 17 and 29. Messian
aimed to create a sense of never-ending time and his music
generates the impression of something unusual and unsettling.
Similarly, the art work of Salvadore Dali demonstrates
the Spanish artist’s interest in the mathematical
idea of fractals, as seen in the painting Visage of War.
Professor du Sautoy managed to successfully debunk the
idea of a dichotomy between the arts and sciences and
show that both draw inspiration from nature but use different
languages, including mathematics, to replicate it.
105 people including staff, alumni, current students and the
general public enjoyed the talk and discussion of this enthusiastically-presented
lecture continued afterwards over
a wine reception.
The 2016 Dame Kathleen Ollerenshaw Lecture will take place on Thursday
13th October, 5.30pm in Lecture Theatre B in University Place.
The lecture will be delivered by Hannah Fry. To book your free space at
Stay connected
the event, please email Jenny Sloan (jenny.sloan@manchester.ac.uk).
2016 Interview Programme winners announced
Every year, the School of Mathematics runs a peerassisted
Interview Programme designed to ensure that students
appraise their application and interviewing skills as
early as possible in their university career.
This year, a selection of our first and second year students
applied for one of three mock internships (business, finance
or technical). These applications were then appraised
and shortlisted by third year, fourth year and postgraduate
students. The applicants went through a rigorous
selection process at the beginning of the second semester,
including psychometric testing and in-tray exercises, before
they were interviewed by our third year, fourth year and
postgraduate interviewers. The interviewers received training
from Ernst and Young, RBS, Willis Towers Watson, FDM
and Amaze on how to effectively shortlist candidates for
interview and how to sit on an interview panel.
Following the interviews, six finalists were chosen out of a
total of 16 interviewed to deliver a five minute
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presentation on the business challenges that either Mercer
or Morgan Stanley will face over the next five years. The
presentations and prize-giving took place on Wednesday
16th March 2016, with all participants receiving certificates.
The six finalists were also awarded £20 Amazon vouchers.
2016 Interview Programme Head of School. winners announced
After deliberation by the judging panel, Molly Reeve (below
left with Professor Peter Duck), a second year Mathematics
and German student was chosen as the overall winner, with
Joseph Leach (below right), a first year MMath student being
awarded second place. Both Molly and Joseph were
awarded their winners' certificates by Professor Peter Duck,
During the summer holidays, Molly will travel to Morgan
Stanley’s offices in Canary Wharf, London for her work
shadowing experience, including a Manchester alumni networking
lunch. Joseph will also take up his prize of work
shadowing with Mercer at their Manchester base, as well as
a networking lunch.
The School of Mathematics congratulates all the participants
of this year’s Interview Programme.
Deep Space, Time, and Probability
By Peter Johnson
Imagine you are betting on some dice being rolled. The dice are fair, however, after a period of time, they are secretly replaced
by weighted dice. Clearly you need to detect this change very quickly and accurately, so you can call your opponent
a cheat or adjust your betting strategy. However, after how many unusual dice rolls would you decide the dice are surely
weighted?
Detecting changes in random processes such as this, as quickly and accurately as possible, is important for many scenarios.
Examples include: detecting a plane using radar; identifying nuclear material at ports; reacting to breakages in atomic
clocks on satellites or; determining when is the best time to buy/sell stocks and shares. Using advanced applied probability,
it is possible to provide an 'optimal' time to stop and
declare that a change has occurred (optimal in the sense
of after the change) with a fixed probability of error.
The previous best image of Pluto taken using the Hubble telescope and an image
from the New Horizons mission 2015.
At The University of Manchester, we have a strong
group in applied probability working on research which
looks at problems of this type. Most recently Prof. Goran
Peskir was involved in helping engineers from NASA
detect an unusual change on-board the New Horizons
space craft which was launched in 2006. One of the satellite’s
main aims was to take the stunning photographs
of Pluto which appeared in the news in late 2015.
The satellite has two on-board quartz clocks which are
relied upon to beam accurate data back to earth. Due to
the speed and gravitational effects of the satellite,
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Einstein's theory of relativity means that the speed of time experienced on the satellite differs from that on earth (on a
much smaller scale this also means that your head is older than your feet). This divergence/error, between the satellite’s
time and the time on earth, began to stabilize as it reached the edge of the solar system as was expected due to the craft
travelling at a constant speed and the gravitational/other external effects diminishing. However, as the craft continued past
Pluto the error appeared as though it had started to drift upwards which scientists found very unusual. They wanted to
know if the upward drift was actually present, or this was just a natural random deviation from its predicted stable level.
Graphs taken from recent NASA paper showing the decreasing offset between the clocks on earth and on the satellite. The second graph shows the
appearance of the upward drift.
Using methods of optimal detection, a team including eminent members of the National Institute for Metrological (science
of measurement) Research based in Turin, were able to declare that a change had occurred and the error had indeed
gained an upwards drift (with a probability of a false positive of 2%). This probability of false positive is also decreasing as
more data is received. Many other statistical methods were used to test for the drift but, unlike with the optimal detection
techniques used, were unable to confidently declare the drift was present from the limited amount of data. These optimal
detection techniques have helped the scientists quickly identify the limits of our understanding of space beyond our solar
system and they are still struggling to explain the observed phenomenon.
The probability group is also involved in helping resolve similar problems for the Galileo project, the first global navigation
system primarily for civilian use, that is being developed by the European Union. The system consists of 30 satellites and
will be fully operational by 2019. On board each satellite there is an incredibly accurate atomic clock (these only last
around 7-9 years so were unsuitable for the New Horizons mission) which is hugely important for precise positioning on the
ground. To take a simplified view of how a GPS system finds a receiver's position on earth, we can assume that all the
clocks are accurate and synchronized. Each of the satellites (3 or
more in range at any one time) then emit a signal containing
their clock’s current time and the satellite’s current location in
space.
This signal (electromagnetic) then travels at the speed of light
(300 million meters per second) to the receiver and the time between
the time of transmission to the time the signal is received
gives the distance between the two. So the receiver knows its
distance away from each satellite and can therefore calculate its
position using a process of 'trilateration' (see diagram to the left
for a 2D representation).
As the signal travels incredibly fast to the receiver, the time between
transmission and it being received is very small. This
means that the clocks on-board need to be very accurate;
Circles showing the distance from each satellite, where the intersection gives the receiver’s position.
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a 10 nanosecond error (a nanosecond is a billionth of a second) can mean that the position is out by up to 30 meters on
the ground. The modern atomic clocks are astonishingly accurate and on earth they have been built so that they lose
one second every 15 billion years. Although the atomic clocks on the satellites are much smaller they are still very accurate
and work as required when they are put into space. However atomic clocks do occasionally see strange errors appear,
the causes of which are not yet fully explained.
If an error is observed, the clocks can be recalibrated as they pass over certain points on earth, however they require on
board detection algorithms to identify quickly and accurately whether an error has appeared. This ensures that the satellites
can temporarily stop transmission until they are recalibrated. This is vital as these systems are used for very important
jobs, including helping to land planes, where accuracy is vital.
In this way, methods from applied probability are helping to land planes, keep you on the road, make scientific discoveries
7.5 billion kilometers way, and letting you know if you are being cheated with weighted dice.
Stay connected
As a graduate of The University of Manchester, you’re a member of our thriving alumni community. In fact, the University
has more than a quarter of a million members worldwide – the largest alumni community of any UK campus-based
university!
That’s why it’s important to keep connected with other alumni across the world. We deliver an array of events, international
networking opportunities, discounts, and volunteering opportunities tailored to your degree and professional and
personal experience. You can also receive some amazing discounts as an alumnus, such as reduced rates across Manchester
retail and hospitality outlets, including our very own Manchester Museum and the award-winning Whitworth Art Gallery.
Remember, you can also get free access to the majority of our University libraries and e-journals, as well as discounted
postgraduate study and access to The Careers Service for two years after graduation!
Want to find out more? Visit Your Manchester, update your details and set your preferences on your dedicated alumni
online portal. Remember, you can also keep in touch with The School of Mathematics via our Alumni and Staff Linked In
Group and the Manchester University Maths Twitter page.
Manchester Gold Mentoring
Manchester Gold is a mentoring programme through which alumni can provide guidance and support to current students
about course and career choices.
Mentoring is an excellent way to share your wisdom and experience
with students, as well as enabling you to develop your own skills. To
find out more, please visit: www.your.manchester.ac.uk/getinvolved/help-students-to-career-success/mentoring
Future Submissions and Contact Details
It was a pleasure to interview two of our former students, Neil Horrocks and Rohana Gunawardena, and we
were delighted to receive so many memories of the Maths Tower from our alumni. Submissions or ideas for
future editions are very welcome, and can be made at any time.
We’re looking for articles about your time here at the University and in Manchester, but also submissions regarding
what you have been up to since graduating, professionally or personally. We would also welcome any
feedback regarding this edition of your newsletter. If you would like to get in touch, please contact Jenny
Sloan; Email: jenny.sloan@manchester.ac.uk; Tel: 0161 275 55812
© 2016 The School of Mathematics, The University of Manchester. Editor: Jenny Sloan. Head of Alumni Relations (Mathematics): Bill Lionheart.
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