MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Biographical Vignettes 173
published posthumously in 1910. M-matrices were named for him by Alexander
Ostrowski. See Property 85 of Chapter 2 for a result on the Minkowski
plane with a regular dodecagon as unit circle. He died suddenly of appendicitis
in Göttingen, aged 44.
Vignette 31 (Helge von Koch: 1870-1924).
Helge von Koch was born into a family of Swedish nobility in Stockholm
[144]. In 1892, he earned his doctorate under Gösta Mittag-Leffler at Stockholm
University. Between the years 1893 and 1905, von Koch had several
appointments as Assistant Professor of Mathematics until he was appointed to
the Chair of Pure Mathematics at the Royal Institute of Technology in 1905,
succeeding Ivar Bendixson. In 1911, he succeeded Mittag-Leffler as Professor
of Mathematics at Stockholm University. Von Koch is known principally for
his work in the theory of infinitely many linear equations and the study of the
matrices derived from such infinite systems. He also did work in differential
equations and the theory of numbers. One of his results was a 1901 theorem
proving that the Riemann Hypothesis is equivalent to a stronger form of the
Prime Number Theorem. He invented the Koch Snowflake (see Propery 60) in
his 1904 paper titled “On a continuous curve without tangents constructible
from elementary geometry”. He died in Stockholm, aged 54.
Vignette 32 (Bertrand Russell: 1872-1970).
Bertrand Russell, 3rd Earl Russell, was born into a liberal family of the
British aristocracy in Trelleck, Monmouthshire, Wales [51]. Due to the death
of his parents, he was raised by his paternal grandparents. He was educated
at home by a series of tutors before entering Trinity College, Cambridge as a
scholar in 1890. There, he was elected to the Apostles where he met Alfred
North Whitehead, then a mathematical lecturer at Cambridge. He earned
his B.A. in 1893 and added a fellowship in 1895 for his thesis, An Essay on
the Foundations of Geometry, which was published in 1897. Despite his previously
noted criticism of The Elements (see opening paragraph of Chapter
1), it was his exposure to Euclid through his older brother Frank that set his
life’s path of work in Mathematical Logic! Over a long and varied career, he
made ground-breaking contributions to the foundations of Mathematics, the
development of formal logic, as well as to analytic philosophy. His mathematical
contributions include the discovery of Russell’s Paradox, the development
of logicism (i.e. that Mathematics is reducible to formal logic), introduction
of the theory of types and the refinement of the first-order predicate calculus.
His other mathematical publications include Principles of Mathematics (1903),
Principia Mathematica with Whitehead (1910, 1912, 1913) and Introduction
to Mathematical Philosophy (1919). Although elected to the Royal Society in
1908, he was convicted and fined in 1916 for his anti-war activities and, as