Thread by @BarbaraFantechi, How do I disagree? Let me count the ways!1. Don't know abt [...]

How do I disagree? Let me count the ways!
1. Don& #39;t know abt maths in general. In my area of expertise the 21st century has brought many wonderful ideas: higher category methods, brilliant new results in moduli theory, perfectoid spaces are just the first that come to mind. 1/ https://twitter.com/3blue1brown/status/1199733437944356865">https://twitter.com/3blue1bro...

https://twitter.com/3blue1brown/status/1199733437944356865

Whether they will be considered equally important a century from now is hard to say. It is equally unclear how much people in 1919 had a clear view of what wpuld be important nowadays: see eg the varying impact of Hilbert& #39;s problems. 2/

Also, all the great ideas are so ikprtant because they haven& #39;t remained isolated: they have been worked on, sharpened, generalized, recontextualized, etc. Often what we use is very far from the original formulation. 3/

2. I also violently disagree on the perspective given on how mathematicians have it better, which ignores completely all the many MANY people who didn& #39;t have ANY access to mathematics at all, and the MANY who still don& #39;t. 4/

All the people who were and are barred from education by lack of money, of medical care/accomodations, by language or cultural boundaries. It& #39;s disingeneous to mention Minkowski dying of appendicitis but not Noether struggling to be a student first, a professor later. 5/

The thread quoted is written by someone who, when he (of course it& #39;s a he) imagines himself 100 years ago, sees a well off, healthy man with access to college. I see my grandma (born 1904) a sharecropper who never went to school and became a live-in maid to escape the farm. 6/

3. More importantly, the whole thread reeks of one of the worst misconceptions about maths (and science!): that it proceeds by BIG IDEAS and GENIUSES (bonus info: in

https://abs.twimg.com/emoji/v2/... draggable="false" alt="🇮🇹" title="Flag of Italy" aria-label="Emoji: Flag of Italy"> the word genio is male only) and no one else counts. 7/

In fact, the opposite is true: none of the geniuses mentioned worked alone, and even the input brilliant people who did work a lot alone (Wiles, Perelman) has been made relevant by a number of others, before and after them. 8/

In my experience, great ideas are collective works, the product of a community stretched across time and space whose collaborations and disagreements, dead ends and rediscoveries gove rise to the best maths, just like times and pressure make carbon into diamonds. 9/

The division between "fundamental ideas by geniuses" and "ordinary research work" is arbitrary and misleading. Fundamental ideas are born by a sequence of ordinary works, and exploted in a series of other ordinary works. There& #39;s a difference in grade, not in essence. 10/

This is something I have to explain, again and again, to incoming Master and PhD students, probably confused by media representations that necessarily shed light on a few people (Ramanujan, Wiles, Nash, Turing). 11/

To see the same written by a colleague is deeply disturbing. Of course, I may well have misinterpreted - Twitter is a very poor medium for nuance! - I probably did. But in case someone else was equally confused, I thought it important to clarify. 12/

My usual #SciComm message is that maths research is in fact exploding, with wave after wave of progress coming up in breathless sequence over the last century, especia
ly after WW2, precisely for the reasons identified. 13/

I am looking forward to a future (that I may not live to see) where all human beings on the planet will have access to research, if they so desire. I am sure this will lead to much better mathematics. I have no fear except the opposite, a restriction of opportunities. /end

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