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Many eminent mathematicians did their best work while not talking about it with anyone, sometimes in isolation. Newton's calculus, Perelman's poincare, much of

Many eminent mathematicians did their best work while not talking about it with anyone, sometimes in isolation. Newton's calculus, Perelman's poincare, much of Grothendiek's work, Wiles's fermat, Ramanujan's earlier days. That's not all top mathematicians as you can look at Von Neumann as a sociable counter-example. But it shows that discussion of your current ideas is not a requirement. Grothendiek goes so far as to say it is a net negative for mathematical creativity because it is difficult to resist thinking like the herd without some level of seclusion.

fultonn 27d ago
> eminent I would use a different adjective: exceptional. There are not not times where lone geniuses produce amazing output. But most of humanity's progress over the last few thousand years (or at least certainly the last few hundred) resulting from a different type of work.
- energy123 27d ago
  That hypothesis requires substantiation. Just because 10 people in a room came up with a breakthrough doesn't mean a sociological process contributed positively to that breakthrough. People generally like socializing, so the base rate is going to be high by default. The breakthroughs might have been more numerous if they had each followed Grothendieck's advice (who is a contender for the world's most talented theory builder) and intentionally decorrelated from one another to free themselves from convention. Referring to my list of examples as exceptional in the sense of being rare is rather unfair, given how numerous these examples are relative to the body of mathematical work we would consider incredible and especially relative to the desire of the average human to socialize. The fact that such a large % of that body of work occurred while the individual was in relative isolation is something we should pay attention to.
  - fultonn 23d ago
    > People generally like socializing If people don't like socializing then your argument not only falls apart, but actually leads us to something like the opposite of the conclusion you found. And people definitely don't like socializing! Because we're not talking about "socializing" in the sense of parties or even water cooler conversations. We're talking about socializing in the context of a group of professionals working together on under-specified problems/solutions. The English word for that type of socializing is: Meetings. Saying that "people like socializing" in the context of professional knowledge work is like saying "people like woodworking" in the context of stick framing cookie cutter developments in Georgia in the summer. I don't think I've ever worked with a productive scientist or mathematician who didn't loathe meetings. In fact, I think I can probably count on one hand the number of people I've met who seem to not loathe meetings. Also: there are pretty powerful social/professional forces -- in Mathematics and related disciplines in particular -- which incentivize people to play into the perception that they are a "lone genius" or at least the "main character". So the group of people we're talking about both hate meetings and have a strong incentive to be perceived as an independent genius/main contributor. And yet the vast majority of good science and mathematics involves large groups of people (who mostly complain about the resulting necessity of meetings, lol). I'll also submit that most of the "lone genius" instances are confounded by the strong social incentive to be perceived as either a lone genius or at least the main contributor. There are at least a few prominent historical examples of math/math-adjacent giants who "worked alone" but were in fact in deep conversation with both the literature and their peers. But, again, there's a lot of gray area, and that's what I meant in my original post when I said "This isn't exactly what I actually think". Two examples of gray area: 1. I'll certainly concede that there are some types of work that do not require that sort of social process to happen. That's the sort of work you seem to be pointing toward here. But opportunity to do that type of work is rare in general, and those opportunities are far more scarce today than it was in 1690 or even 1990. 2. There are also some types of work where the corresponding sociological process is pretty simple and is probably sufficiently captured. So I'm not bearish about what's possible, at least per se. But technology executives and analysts in particular have some really fundamental misunderstandings about how this type of labor works in most cases, and I see some of those same misunderstandings among lots of professional mathematicians.

fultonn 27d ago

> eminent I would use a different adjective: exceptional. There are not not times where lone geniuses produce amazing output. But most of humanity's progress over the last few thousand years (or at least certainly the last few hundred) resulting from a different type of work.

energy123 27d ago
That hypothesis requires substantiation. Just because 10 people in a room came up with a breakthrough doesn't mean a sociological process contributed positively to that breakthrough. People generally like socializing, so the base rate is going to be high by default. The breakthroughs might have been more numerous if they had each followed Grothendieck's advice (who is a contender for the world's most talented theory builder) and intentionally decorrelated from one another to free themselves from convention. Referring to my list of examples as exceptional in the sense of being rare is rather unfair, given how numerous these examples are relative to the body of mathematical work we would consider incredible and especially relative to the desire of the average human to socialize. The fact that such a large % of that body of work occurred while the individual was in relative isolation is something we should pay attention to.
- fultonn 23d ago
  > People generally like socializing If people don't like socializing then your argument not only falls apart, but actually leads us to something like the opposite of the conclusion you found. And people definitely don't like socializing! Because we're not talking about "socializing" in the sense of parties or even water cooler conversations. We're talking about socializing in the context of a group of professionals working together on under-specified problems/solutions. The English word for that type of socializing is: Meetings. Saying that "people like socializing" in the context of professional knowledge work is like saying "people like woodworking" in the context of stick framing cookie cutter developments in Georgia in the summer. I don't think I've ever worked with a productive scientist or mathematician who didn't loathe meetings. In fact, I think I can probably count on one hand the number of people I've met who seem to not loathe meetings. Also: there are pretty powerful social/professional forces -- in Mathematics and related disciplines in particular -- which incentivize people to play into the perception that they are a "lone genius" or at least the "main character". So the group of people we're talking about both hate meetings and have a strong incentive to be perceived as an independent genius/main contributor. And yet the vast majority of good science and mathematics involves large groups of people (who mostly complain about the resulting necessity of meetings, lol). I'll also submit that most of the "lone genius" instances are confounded by the strong social incentive to be perceived as either a lone genius or at least the main contributor. There are at least a few prominent historical examples of math/math-adjacent giants who "worked alone" but were in fact in deep conversation with both the literature and their peers. But, again, there's a lot of gray area, and that's what I meant in my original post when I said "This isn't exactly what I actually think". Two examples of gray area: 1. I'll certainly concede that there are some types of work that do not require that sort of social process to happen. That's the sort of work you seem to be pointing toward here. But opportunity to do that type of work is rare in general, and those opportunities are far more scarce today than it was in 1690 or even 1990. 2. There are also some types of work where the corresponding sociological process is pretty simple and is probably sufficiently captured. So I'm not bearish about what's possible, at least per se. But technology executives and analysts in particular have some really fundamental misunderstandings about how this type of labor works in most cases, and I see some of those same misunderstandings among lots of professional mathematicians.