From: "Nittai Madrid" Subject: Re: Smith & Klein comments Date: Fri, 22 Jan 1999 11:41:57 PST Re: (to John Klein) Well, I'm interested in the question "What is mathematics?", and I'm actually just starting my PhD. I think this kind of question is very interesting in part because nobody seems to be able to answer it properly. Even those answers that give some kind of intellectual pleasure can't claim to be all that illuminating, and of course if mathematicians can't answer them, nobody else will. N Madrid Cambridge >____________________________________________________________ >Date: Fri, 22 Jan 1999 12:51:52 -0500 (EST) >From: "John R. Klein" >Subject: Re: 6 more comments > >I always had the (perhaps false) impression that research mathematicians >only concern themselves with the questions like "What is Mathematics?" >after their own research fizzles out. Is everyone who posts to this list >coasting into an early retirement? > >John R. Klein > > ______________________________________________________ Subject: Re: Smith & Klein comments Date: Fri, 22 Jan 1999 15:14:24 -0500 From: "Clarence W. Wilkerson" In response to Klein: That's unfortunately the kind of smartass remark for which I am well known. On the other hand, as someone who has served for over twenty years on departmental and university promotion committees, one is often called on to give a sound bite about mathematics or topology to one's non-mathematical or non-topological colleagues. So I don't think one should try to trivialize the discussion. I often find myself in the tight circle that "mathematics is what mathematicians do" and "people who do mathematics are mathematicians". This comes up particularly in discussions of applied math versus engineering. Clarence Wilkerson ______________________________________________________- From: Tibor Beke Subject: Re: Smith & Klein comments Date: Fri, 22 Jan 1999 21:23:03 +0100 (MET) There are examples and there are counterexamples. People working in fields that resist formalization (thus, the "easy" answer to "What am I doing here?") tend to have to face the question earlier. I have geometers in mind. Your namesake, Felix Klein, gave his famous "Erlangen Program" (on what the subject of geometry is) when he was active (and what a good answer he gave, many decades before Einstein: it's the study of invariants under groups of motion). Poincare is well-known for his writings on the philosophy of science, and he had some of his deepest mathematical ideas right before his death. Hilbert wrote "Foundations of Geometry" in 1899, when he wasn't completely brain-dead either. Most people think Brouwer went overboard in forsaking topology for foundations, but those who have studied his early work assert that foundational concerns were on his mind even then; for many years, he simply kept it to himself or communicated orally. On the very opposite (i.e. very formal) side, Godel asserted that his finding the (in)completeness theorems was very much assisted by his Platonism (so we are talking of his first published works here, though he came "out of the philosophical closet" much later). In 1930, there was a conference on the philosophy of mathematics where the formalist standpoint was defended by John Neumann... and he was HARDLY burnt out. But I buy it, by and large, that one is talented either as a theoretician or as a practitioner of one's art; here I take mathematicians to be creative artists, and there are many instances of that statement to be found in music, painting or even film directing too. Tibor B. ______________________________________________________- Date: Fri, 22 Jan 1999 16:37:41 -0500 (EST) From: "John R. Klein" Subject: Response to Clarence I originally sent the below as a direct reply to Clarence. I decided after that I should actually post it to the top-list. ---------- Forwarded message ---------- Date: Fri, 22 Jan 1999 16:25:57 -0500 (EST) From: John R. Klein To: wilker@math.purdue.edu Subject: Re: Smith & Klein comments Hi Clarence, I didn't intend to be a smartass in my post. I think that taking up the question "What is Mathematics?" is indicative of the way that the mathematics community is preoccupied with the problem of justifying itself. I personally don't feel compelled to try to answer this question (okay, I'm not yet on any committees), because the answers to it (i.e., the top-list posts) **rarely** reflect the actual activity which we as mathematicians pursue. I bet that the problem of explanation doesn't exist in the same way in the other sciences---it's less painful to cook up explanations for the lay public. Maybe I'm wrong here. Even when I do try to contrive a (trivialized) explanation of what mathematics is about (to a non-mathematical colleague say), I have heard replies like, "What are the pratical applications of that?" which of course is completely beside the point. How come no one ever asks this last question in reference to the game of football? Best, John