March 2006 - mathfun@mailman.xmission.com

[math-fun] a mathematician under the influence
by James Propp 02 Mar '06

02 Mar '06

If we refine the question to something like "Who would be most successful in leading a campaign to automate proof-checking in huge swaths of mathematics?", then I'll start the bidding by nominating David Mumford. His experience as an algebraic geometer makes him eminently qualified to assess just how deep mathematics can get, and his more recent work with computer vision makes him credible as an authority on what current methods of automation might be able to achieve. Don Knuth would also be plausible as the leader of such a automation crusade. As a computer scientist, he has a keen understanding of what it takes to create a software system. And, to the extent that his personal style and his sense of design contributed to the success of TeX, one might predict that he'd use the same flair to develop and promote a general- purpose proof-verification system for mathematicians. If the impulse behind the question is "Who's the one person in the world such that, if I convince him, he'll convince everyone else?", there's a catch: It could be that the more qualified someone is to say "This is something we mathematicians can and should do" and get people to take notice --- that is, the more knowledgeable he/she is about what math is, and what early 21st century computers can do --- the less likely it is that he/she would say it. Jim Propp

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RE: [math-fun] Most influential mathematician?
by Jud McCranie 02 Mar '06

02 Mar '06

I think Clifford Pickover solicited nominees for this several years ago. Anyone remember?

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[math-fun] Influential mathematicians
by Steve Gray 02 Mar '06

02 Mar '06

The majority of the much less than 1% of the general public who has heard of any contemporary mathematician would probably name Andrew Wiles. Of course we're probably not talking about a popularity contest, but if we were, J.H. Conway's name would also come up. I wouldn't include those like Gardner who are mostly popularizers, as valuable as they are. Steve Gray

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[math-fun] Most influential mathematician?
by Henry Baker 02 Mar '06

02 Mar '06

Does anyone on this list have a suggestion of who is the most influential mathematician today? I'm looking for someone of the stature of Hilbert; i.e., someone whom most people inside & outside of mathematics would acknowledge as being influential. Of course, this presumes that anyone outside of mathematics knows or cares about mathematicians! For example, during WWII, Einstein was considered the most influential of physicists by people inside & outside of the physics community. Thanks in advance for any suggestions. Henry Baker

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Re: [math-fun] Most influential mathematician?
by dasimov＠earthlink.net 02 Mar '06

02 Mar '06

Henry writes: << Does anyone on this list have a suggestion of who is the most influential mathematician today? I'm looking for someone of the stature of Hilbert; i.e., someone whom most people inside & outside of mathematics would acknowledge as being influential. Of course, this presumes that anyone outside of mathematics knows or cares about mathematicians! . . . >> As you suggest, there is little overlap between the most influential mathematicians and the ones most known to the general population. So it may be necessary to narrow down what you're asking for some more. You said most influential *today*, but not that the mathematician need be alive today. I'm not sure what you meant regarding this. Shiing-Shen Chern, the differential geometer (1911-2004) is said to be well-known to the general population of China. Cf. <http://en.wikipedia.org/wiki/Chern>. Martin Gardner (mostly self-taught in math) and Ian Stewart are widely known as popularizers of math; many mathematicians attribute their choice of profession to Gardner's columns in Sci. Am. Within math per se, I think of John Milnor and Jean-Pierre Serre as probably the most influential mathematicians alive today. (I'd pick Milnor over Serre, because Milnor's scope is probably wider and he's written more math texts, all of which are gems of exposition, and accessible survey articles.) Excluding Euclid, Pythagoras, Archimedes, and Al-Khwarizmi for being in different categories, I'd say that Carl Friedrich Gauss is the clear winner, if the question is which mathematician living or dead, has had the most impact on modern civilization AND within math per se. Cf. <http://en.wikipedia.org/wiki/List_of_topics_named_after_Carl_Friedrich_Gauss> for evidence of this. (Full disclosure: I would've said Gauss anyway, but recently learned from the Mathematics Genealogy Project that Gauss is a direct mathematical ancestor of mine, i.e., via a sequence of thesis advisors.) --Dan

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Re: [math-fun] Stirling Numbers?
by dasimov＠earthlink.net 01 Mar '06

01 Mar '06

Thanks, everyone, for the interesting asymptotic expressions for B(n). (Would only that they were expressed purely in terms of n, rather than a root of some weird equation in n.) --Dan

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Re: [math-fun] Stirling Numbers?
by N. J. A. Sloane 01 Mar '06

01 Mar '06

Dan, the entry for the Bell numbers is A000110 there you will find: %F A000110 a(n) is asymptotic to n!*(2 Pi r^2 exp(r))^(-1/2) exp(exp(r)-1) / r^n, where r is the p\ ositive root of r exp(r) = n. - see e.g. the Odlyzko reference. Neil

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Re: [math-fun] Polyomino question
by Michael Reid 28 Feb '06

28 Feb '06

> What is the smallest polyomino that contains all polyominos of size n? > For n = 4, there is a unique size 6 polyomino that works: > OOOO > OO XX XXXX also works. it is clear that size 6 is the smallest possible, because the square tetromino and the straight one can overlap in at most two squares. > For n = 5, the best I can do is 9: > O > OOOOO > OOO > I don't know if this is unique; I would be very surprised if 8 is possible. X XXXXX XXX also works. it is easy to show that size 8 is indeed impossible. note that the "I" and "W" pentominoes can overlap in at most 2 squares, so at least 8 squares are required to accommodate even those two. there are only a handful of ways to overlap them, covering as few as 8 squares, and none of the resulting shapes contain the "X" pentomino: W W W W W W W W WW WW WW WW BBIII IBBII IIBBI IIIBB BBIII IBBII IIBBI IIIBB WW WW WW WW a simple back-of-the-envelope type calculations shows that the only 9-ominoes that work are the two above. what i did was: add a single square to each of the above octominoes in a way that would also accommodate the X pentomino, and check those shapes. there were 15 resulting 9-ominoes (one occurred twice) and only 2 contain all pentominoes. i also tried all ways of overlapping the I and W pentominoes in a single square (9 ways) but none of the shapes contains the X pentomino. i realize that this approach is prone to error, so it would be nice to have independent confirmation. i haven't examined the hexomino case yet, but it seems unlikely to succumb to such a simple analysis. mike

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