Humanist Discussion Group, Vol. 34, No. 14.
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        Date: 2020-05-12 13:13:01+00:00
        From: Willard McCarty 
        Subject: against 'knowledge production'

As antidote to the notion of 'knowledge production' (as if in a
factory), allow me to recommend two chunks of text from two
mathematicians. The first is from a wonderful paper by the American
topologist William Thurston (1946-2012), "On proof and progress in
mathematics"*. The other is a comment, during a long three-way
conversation, by the French geometer and mathematical physicist André
Lichnerowicz (1915-1998)**. Both are at pains to stress the process that
motivates them. In the passage that follows first, Thurston focuses on
the social process, giving a sense to the much used term 'collaboration'
that I think works especially well for the humanities. Like Thurston,
Lichnerowicz gives due recognition to the gold standard of modern
Western mathematics, proof, but in the second passage directs attention
to the process of getting there, the process from which comes his real
motivation.

(1) Thurston, pp. 11-12:

> I think that our strong communal emphasis on theorem-credits has a
> negative effect on mathematical progress. If what we are accomplishing
> is advancing human understanding of mathematics, then we would be
> much better off recognizing and valuing a far broader range of
> activity. The people who see the way to proving theorems are doing it
> in the context of a mathematical community; they are not doing it on
> their own. They depend on understanding of mathematics that they
> glean from other mathematicians. Once a theorem has been proven, the
> mathematical community depends on the social network to distribute
> the ideas to people who might use them further—the print medium is
> far too obscure and cumbersome.
>
> Even if one takes the narrow view that what we are producing is
> theorems, the team is important. Soccer can serve as a metaphor.
> There might only be one or two goals during a soccer game, made by
> one or two persons. That does not mean that the efforts of all the
> others are wasted. We do not judge players on a soccer team only by
> whether they personally make a goal; we judge the team by its
> function as a team.
>
> In mathematics, it often happens that a group of mathematicians
> advances with a certain collection of ideas. There are theorems in
> the path of these advances that will almost inevitably be proven by
> one person or another. Sometimes the group of mathematicians can even
> anticipate what these theorems are likely to be. It is much harder to
> predict who will actually prove the theorem, although there are
> usually a few “point people” who are more likely to score. However,
> they are in a position to prove those theorems because of the
> collective efforts of the team. The team has a further function, in
> absorbing and making use of the theorems once they are proven. Even
> if one person could prove all the theorems in the path
> single-handedly, they are wasted if nobody else learns them.

(2) Lichnerowicz, p. 25:

> Yet, it is not for these reasons, namely to produce rigorous and
> compelling proofs, that one becomes a mathematician. Every
> mathematician, within himself and even with a few close colleagues,
> conducts a discourse that has nothing to do with that. We must draw a
> clear distinction between the discourse of universal communication
> and the discourse of creation in mathematics. According to general
> consensus, when a mathematician works, he is in fact reflecting upon
> a certain field in which he encounters mathematical beings, and ends
> up playing with them, until they become familiar to him. He can then
> work while taking a walk or while conversing with a boring
> interlocutor. This is a somewhat draining activity which we have all
> experienced. After a time, be it a month or a year, either we get
> nowhere, finding nothing, or else we manage to get hold of some
> result. Then begins the onerous task - the obligation to write up for
> the benefit of the mathematical community a polished article that is
> as compelling as possible.
>
> As a result, there are two types of activity. If one becomes a
> mathematician it is for the creative activity, the game of intuition,
> and not at all for the burden of publishing. Too often the two are
> confused.

Comments?

Yours,
WM
-----
*https://arxiv.org/abs/math/9404236v1; cf.
www.ams.org/notices/201511/rnoti-p1318.pdf
**Alain Connes, André Lichnerowicz and Marcel Paul Schützenberger,
Triangle of Thoughts, trans. Jennifer Gage (American Mathematical
Society, 2000), https://archive.org/details/triangleofthough0000conn;
cf. https://www.ams.org/notices/200902/rtx090200244p.pdf

--
Willard McCarty (www.mccarty.org.uk/),
Professor emeritus, Department of Digital Humanities, King's College
London; Editor, Interdisciplinary Science Reviews
(www.tandfonline.com/loi/yisr20) and Humanist (www.dhhumanist.org)




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