主催：慶應義塾大学　論理と感性のグローバル研究センター

Jeremy Gray short bio:

Jeremy Gray is an Emeritus Professor of  The Open University and an
Honorary Professor in the Mathematics Department at the University of
Warwick. His research interests are in the history of mathematics,
specifically the history of algebra, analysis, and geometry, and
mathematical modernism in the 19th and early 20th Centuries. The work
on mathematical modernism links the history of mathematics with the
history of science and issues in mathematical logic and the philosophy
of mathematics.

He was awarded the Otto Neugebauer Prize of the European Mathematical
Society in 2016 for his work in the history of mathematics, and the
Albert Leon Whiteman Memorial Prize of the American Mathematical
Society in 2009 for his contributions to the study of the history of
modern mathematics internationally. In 2012 he was elected an
Inaugural Fellow of the American Mathematical Society. In 2010 he was
one of the nine founder members of the Association for the Philosophy
of Mathematical Practice (APMP).

He is the author of eleven books, of which among the most recent are
Plato’s Ghost: The Modernist Transformation of Mathematics (Princeton
U.P. 2008), Henri Poincaré: a scientific biography  (Princeton 2012),
and The Real and the Complex (Springer 2015). Two more books are to be
published in 2018: Under the Banner of Number: A History of Abstract
Algebra, by Springer, and Simply Riemann in the Simply Charly series
of e-books.

Abstracts:

 Poincaré on proof and understanding

Poincaré has an exaggerated reputation not being rigorous in his work.
In this talk I shall show that he cared about rigour in mathematics,
but had justified criticisms of it. However, the more important task
was to understand mathematics and physics, and this meant to be
enabled to discover new ideas. Certainty in abstract mathematics was
provided by the principle of recurrence, which imposed limits on any
theory of sets. Thereafter, a pragmatic sense of certainty was
provided in applied mathematics and physics by the use of conventions.
Conventions, he believed, govern our choice of a geometry for space
and the choice of the laws of mechanics and other branches of physics.
Objectivity, he said, depended on discourse, and I shall argue that
Poincaré’s fundamental position is that the use of mathematics in
science is close to Wittgenstein’s idea of a language game.

 
 The philosophy of Hermann Weyl


By 1910, the year he turned 25, Weyl was developing a finitist
philosophy of mathematics, based on a logical theory of relations. He
also believed that the human mind can understand ideas only
sequentially. He developed this approach on his book The Continuum
(1918), and for a time came close to agreeing with Brouwer’s
intuitionism, but he abandoned them in the mid-1920s when he became
involved in exploring the theory of Lie groups. He then had to turn
back towards Hilbert’s ideas about mathematics and physics, and
developed his own theory of what he called the symbolic universe in
which mathematics and physics supported each other in complementary
ways. Weyl sought a unified philosophy that would govern not only his
scientific practice but be rooted in a theory of knowledge and an
understanding of how it is acquired.

Jeremy Gray

Open University, Milton Keynes, MK7 6AA, U.K. and University of
Warwick, Coventry, CV4 7AL, U.K.