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History of Mathematics / Histoire des mathématiques
(Org: Thomas Archibald, Acadia University)
- THOMAS ARCHIBALD, Acadia University
Hilbert and Bernstein
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Hilbert's nineteenth and twentieth problems proposed themes related to
partial differential equations. The nineteenth problem asked whether
certain variational problems, described as "regular", must always
have analytic solutions. The twentieth problem posed very generally
the issue of existence of solutions for boundary value problems; in
stating it, Hilbert proposed the idea of generalized (or weak)
solutions. These problems were taken on by Serge Bernstein, who
studied both in Paris and in Göttingen. Bernstein assembled
methods from the French context (Poincaré's continuity method) with
Hilbert's ideas and made decisive contributions to the solution of
both problems, in particular using a priori estimates in a way
that was not fully appreciated until Schauder grasped the method in
the 1930s. The paper will sketch these events.
- EISSO ATZEMA, University of Maine
Lessons on Train Schedules: From String Charts to Teaching
Tools
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One of the major developments in early 20th-century mathematics
teaching is the inclusion of the function concept and its graphical
representation. In this talk I will discuss the curious history of
one particular kind of graph, the so-called string chart or train
graph. I will trace the rise and fall of the string chart from its
mid-19th century beginnings as a tool to scheduling trains via a
public convenience to a mere application in a number of mathematics
textbooks of the first decades of the 20th century. Emphasis will be
on the striking differences in the reception of the train graph as a
teaching tool between the European Continent and the English-speaking
countries.
- FERNANDO GOUVEIA, Colby College, Dept of Mathematics, Waterville, ME 04901, USA
After the Marquis: the post-history of L'Hospital's rule
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When most historians discuss "L'Hospital's Rule", they focus on the
story of Bernoulli's letters to L'Hospital and of their
"arrangement". When one actually looks at their work, however, it
becomes clear that L'Hospital's "L'Hospital's Rule" is very
different from what one finds in current books. There is no reference
to limits, the proof does not involve the mean value theorem, and there
is no "infinity over infinity" case. This talk is a preliminary
report on joint work with Colby student Melissa Yosua investigating
the post-L'Hospital history of the "rule".
- HARDY GRANT, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3
Mathematics in Plato's Thought
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It is a commonplace that among the great philosophers Plato assigned
unusual significance to mathematics. I shall attempt an overview,
taking into account both the intellectual context and the social
milieu. My central theme will be the place of mathematics in the
origin and subsequent career of the theory of Forms-a more complex
and interesting tale than it might seem. As time allows I shall try
to touch on related issues, especially Plato's conception of the role
of mathematics in education.
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