4 ms·
> 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 so
by JadeNB 7y ago
> 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.
- kragen 7y agoI 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.
- JadeNB 7y ago> 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.)