NEWSLETTER

The EMS Jubilee: Challenges for the
Next 25 Years
Editorial
Richard Elwes (EMS Publicity Officer; University of Leeds, UK))
The roots of mathematics, like those of humanity itself,
lie in Southern Africa. At the dawn of civilisation,
thinkers in Mesopotamia and Egypt made early breakthroughs
in notation and technique. Indian and Chinese
mathematicians produced insights which remain with us
today, while the Persian and Arabic traditions developed
the subject over hundreds of years. Today, as in so many
areas of life, the USA is a modern powerhouse. But, in
our desire to give credit where it is due, and to honour
the contributions of cultures which are too often overlooked,
we should not get carried away. Our own continent
of Europe has been home to a multitude of mathematical
advancements since the time of Pythagoras. Just
occasionally, it is worth reflecting and celebrating this
glorious tradition.
Indeed, many European nations have their own illustrious
mathematical histories. In the 19th and early 20th
centuries, this led to the founding of plethora of national
and regional mathematical societies, of which the oldest
surviving is the Dutch Koninklijk Wiskundig Genootschap,
founded in 1778. The European Mathematical Society
is thus a latecomer, not born until 1990 in the Polish
town of Mądralin. This year therefore, our society has
reached 25 years of age, a youthful milestone which was
celebrated in magnificent style at the Institut Henri Poincaré
in Paris, on 22nd October. The day opened with an
address from the Society’s President, Pavel Exner, and
comprised 4 plenary talks followed by a panel discussion
on the state of European mathematics, as we look to the
challenges of the next 25 years and beyond. Several of
the themes from that conversation were well represented
in the day as a whole, and perhaps it is worth drawing
them out.
A major focus was the need for mathematics to be an
outward-facing discipline, in several senses. Every aspect
of today’s society is influenced by life-transforming technologies
whose design and operation relies on sophisticated
mathematics. According to recent reports in UK,
France, and Netherlands, the economic impact of Mathematics
is enormous, to the tune of 9% of all jobs and 16%
of Gross National Product. The market thus presents an
unprecedented and growing demand for mathematical
expertise, with data science in particular being an area of
explosive growth.
In his plenary talk, Andrew Stuart spoke eloquently
about one pressing challenge in this arena: the relationship
between mathematical models and data. Taking the
example of numerical weather forecasting, a technology
as technically demanding as it is socially important, he
discussed the difficulty of incorporating observational
data into theoretical models, giving appropriate weight
The guests for the EMS Jubilee at Institut Henri Poincaré.
Photo courtesy of Elvira Hyvönen.
to both. He offered the opinion that mathematicians today
stand in a similar position relative to Data, as they
did to Analysis in the time of Fourier: we already have
the basic language and techniques, but a revolution is
surely imminent.
Why do mathematicians do mathematics? In truth,
the answer is not usually because of its societal benefits
or economic impact. At an individual level, we do it because
we enjoy it. Depending on your perspective, we are
either playful people who enjoy amusing ourselves with
puzzles, or deep-thinkers who provide answers to some
of the most profound questions our species can ask. (The
paradox of our subject is that this distinction is, in fact, no
distinction at all.)
The day saw two talks in this vein. The opening lecture
by Hendrik Lenstra was an entertaining investigation
of profinite number theory, meaning the structure
of Ẑ, the profinite completion of the integers. One delightful
discussion involved the profinite extension of
that staple of recreational mathematics, the Fibonacci
numbers. Generations of school-students and lay-people
have been amused by this recursive sequence, and as
Lenstra showed, there is plenty of enjoyment to be had
for professional mathematicians too. (See his essay in the
Newsletter of the European Mathematical Society 61,
September 2006, 15–19.)
In the afternoon session, we were treated to a talk from
László Lovász on geometric representations of graphs.
Here were beautiful problems and deep theorems, whose
origins lie in puzzles accessible to school-children. He began
with the theorem of Koebe that every planar graph
has a circle representation: a set of non-overlapping discs
EMS Newsletter December 2015 3