> I don't know of a single mathematician who has ODed on amphetamines, and only one who voted for Trump (Dan Kleitman)
I'm a mathematician who thinks that your sequence of posts here isn't serving the purpose you seem to think it does. I don't think that addressing it point by point serves much purpose, but these two claims bothered me particularly, so I single them out for response.
I speak to your second point first: surely you don't think that there is only one mathematician who voted for Trump? Unless you do, it is irrelevant that you only know one; there are surely lots of others out there. I didn't, and I don't know any mathematician that I know did, but I know at least a few mathematicians who I know voted for GWB, and I imagine that there have to be at least a few other Trump voters in my mathematical circle.
The first part in particular, in addition to the same quibble about what it matters whether or not you personally know such people (as opposed to whether or not they exist), probably requires an overly restrictive definition of 'mathematician' as "someone with academic credentials, or other official recognition, as a practitioner of mathematics". I personally don't think that's a good definition of a mathematician, and I don't think that advancing such definitions is a good thing for the future of our profession.
Who is "a mathematician"? I definitely don't mean "someone with academic credentials or other official recognition"; surely Erdős was a mathematician when he was a teenager, Ramanujan was a mathematician before he wrote to Hardy, and Lagrange was a mathematician when he discovered the variational calculus with Euler; I think it's even reasonable to assert that Socrates was a mathematician when he taught Menon how to draw a line of length √½, because he demonstrated the correctness of the construction mathematically rather than just asserting it, even though he surely did not discover it at that moment. I think it's sufficient to be doing mathematics as an end in itself.
But that doesn't help much; what does it mean to be "doing mathematics"? Is it sufficient to read a proof? How about reconstructing a proof you vaguely remember? How about working some exercises in a textbook? Does it matter if the exercises are arithmetic or differential equations? What about when Martin Gardner rediscovered some well-known theorem or other? Might it even be sufficient to be doing mathematics for some other purpose, such as predicting the motions of the planets or the flight of an artillery shell, rather than an end in itself?
It seems that there's unavoidably a gray area; the toddler who counts "one, two, three, seven, ten" is definitely not "doing mathematics", while Scholze was surely "doing mathematics" when he discovered perfectoid spaces. Somewhere in between, there are cases where you can plausibly make an argument either way. (I don't think Ramanujan before his contact with Hardy is one of them, but perhaps that's self-serving bias on my part — I have no academic credentials of any kind, other than publications.)
But that's okay. Language isn't math, so we can't expect people to come to a perfect consensus about what it means, although we can of course attempt to clarify our thinking, however much the non-mathematicians may detest and attempt to sabotage such activity.
So, what do you think is a good definition of "a mathematician"?
> So, what do you think is a good definition of "a mathematician"?
It depends on the context. The definition I'd like to advance is that a mathematician is someone who does mathematics (and that what one usually means by "a mathematician" is something more like "one who habitually does mathematics, or one whose profession is the doing of mathematics"); the toddler, while counting "one, two, three", is a mathematician, who may turn into a new-language learner when continuing "seven, ten", or may still be a mathematician if that toddler is fascinated by and exploring number patterns. By this definition, almost everyone is a mathematician at some time or other, so that making claims about what the population of mathematicians does is little more than making claims about what everyone does.
There are at least two problems with this definition: (1) it shifts the question from "who is a mathematician?" to "what is doing mathematics?"; and (2) it blurs meaningful distinctions between people who are habitual or professional mathematicians, among amateurs, dabblers, and tyros, and other distinctions that one might want to make. My answer to (1) is that I would give an equally broad answer to the latter question, and my answers to (2) are twofold, namely (a) tough, and (b) the distinctions can be preserved by including additional modifiers, as I have done. This resolves these problems to my satisfaction, but I don't expect them to satisfy everyone, or even many.
> I don't think Ramanujan before his contact with Hardy is one of them, but perhaps that's self-serving bias on my part — I have no academic credentials of any kind, other than publications.
That sounds self-defeating, rather than self-serving! Why not recognise Ramanujan as a mathematician before Hardy? Surely the same genius was there, just not expressed in familiar ways; so what Hardy can be said to have done to Ramanujan is surely not to have turned him into a mathematician, but instead to have taught him the common language of mathematics in which to express what he already knew but couldn't fully communicate to others.
I didn't mean to assert that young Ramanujan was clearly not a mathematician — rather the opposite!
Perhaps in practice my definition of "a mathematician" is "someone who, when wrong, responds to disagreement by changing their mind rather than becoming defensive or downvoting you", an event I see on a daily basis in lectures on mathematics and very rarely outside of them.
> Perhaps in practice my definition of "a mathematician" is "someone who, when wrong, responds to disagreement by changing their mind rather than becoming defensive or downvoting you", an event I see on a daily basis in lectures on mathematics and very rarely outside of them.
Mathematicians are often OK at this within their discipline, but we're as bad as anyone else at it when dealing with human affairs. (At least, I am.) I might rather suggest the less flattering characterisation of a mathematician who will argue with a statement with which they agree, just to see if it breaks. (At least, I do.)
I'm a mathematician who thinks that your sequence of posts here isn't serving the purpose you seem to think it does. I don't think that addressing it point by point serves much purpose, but these two claims bothered me particularly, so I single them out for response.
I speak to your second point first: surely you don't think that there is only one mathematician who voted for Trump? Unless you do, it is irrelevant that you only know one; there are surely lots of others out there. I didn't, and I don't know any mathematician that I know did, but I know at least a few mathematicians who I know voted for GWB, and I imagine that there have to be at least a few other Trump voters in my mathematical circle.
The first part in particular, in addition to the same quibble about what it matters whether or not you personally know such people (as opposed to whether or not they exist), probably requires an overly restrictive definition of 'mathematician' as "someone with academic credentials, or other official recognition, as a practitioner of mathematics". I personally don't think that's a good definition of a mathematician, and I don't think that advancing such definitions is a good thing for the future of our profession.