Fwd: ***CSHPM Online Colloquium: David Waszek***

[Nicolas Fillion]

The Canadian Society for History and Philosophy of Mathematics (http://www.cshpm.org/) invites members as well as the broader scholarly community to the next talk in our online colloquium series via Zoom. Participants are encouraged to become members (for as little as $10-$30/year, depending on your employment status), but it is not required. Non-members can get regular updates on our activities by liking us on Facebook (https://www.facebook.com/cshpmschpm). The talk will last 30 minutes, followed by a Q&A.

DAVID WASZEK, Postdoctoral researcher at McGill, will deliver the eleventh talk of the CSHPM Online Colloquium series.

DATE: February 19th
TIME: UTC 19:00; Vancouver 11:00; Edmonton 12:00; Regina/Winnipeg 13:00; Montreal/Toronto 14:00; Halifax 15:00; St. John's 15:30

TITLE: Notational differences, exploration and discovery in mathematics
ABSTRACT: Drawing on the analysis of a historical episode of
notation-driven mathematical discovery, I attempt to understand how it
is that apparently innocent notational choices can in fact shape the
course of mathematical research. The historical episode in question
centers on Leibniz and Johann Bernoulli's discovery of an 'analogy'
between the powers of a sum and the differentials of a product, i.e.,
between the formulas for (x+y)^e and d^e(xy); this discovery seems
closely related to Leibniz's introduction of an 'exponential' notation
for differentials (d²x for ddx, d³x for dddx, d⁻¹x for ∫x, etc.). I show
that the notation itself—independently of the conceptual motivations
Leibniz may have had to introduce it in the first place—did indeed play
a part in this discovery and subsequent ones, but that its contribution
cannot not be understood, as is often suggested in the literature, in
terms ‘expressive power’: it is not true that the new notation allows
expressing things that could not be expressed without it. Instead, I
pinpoint two contributions that the notation did make: it brought out a
pattern in a particular formula which would have been less
salient—harder to notice—otherwise; and it transformed what could be
expressed in simple ways, thereby reorienting subsequent exploration.
This second contribution is, I submit, of broader significance, and
suggests a fruitful parallel with *conceptual* change: by transforming
what can be expressed simply, a notational change can, so to speak,
reorganize the landscape that the mathematician explores—impacting not
just what symbolic manipulations are easily accessible, but also what
conjectures are seen as plausible and even what can reasonably be
considered as a single, unitary theorem.



Please distribute this information to all who might be interested. The information to join the session via Zoom is as follows:

Topic: CSHPM Online Colloquium: David Waszek
Time: Feb 19, 2021 11:00 AM Pacific Time (US and Canada)

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