Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) / Chapter Skim
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22. Either It's True, or Else It Isn't
22. Either It's True, or Else It Isn't
Pages 350-361
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From page 350... ...
, after 120 years among the mathematicians, has got the attention of the physicists. Riemann's own imagination was, as I noted in Chapter lO.i, very much that of a physical scientist.
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From page 351... ...
He'd just sIogge(1 through the (differential equations, creating a sort of ad hoc, embryonic operator theory for himself. Still, it's hard to believe that a mind as acute and penetrating as Riemann's woul(1 have missed the analogy between the zeta zeros strung out on the critical line, and his spectrum of perturbation frequencies the analogy that was so dramatically paralleled over afternoon tea in Fuld Hall 113 years later!
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From page 352... ...
Other attendees included the current superstar of math, Andrew Wiles, famous for having proved Fermat's Last Theorem; Harold Edwards, whose definitive book on the zeta function I have mentioned several times in these pages; and Daniel Bump, one of the two names attached to the most euphonious of all RH-related results, the BumpNg Theorem.l34 The AIM has been a considerable force in assaults on the RH during recent years. The Courant conference was the third they had sponsored on RH-related topics.
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From page 353... ...
Another privately-funded enterprise similar to AIM began on the East Coast of the United States in 1998, when Boston businessman Landon T Clay and Harvard mathematician Arthur Jaffe established the Clay Mathematics Institute (CMI)
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From page 354... ...
Whatever may be the case with the other six problems, $1 million is very little extra incentive to prove, or disprove, the Hypothesis. It is sufficiently established as the open problem in math at the beginning of the twenty-first century that whoever can resolve it will attain, in addition to everlasting fame, financial success in lecture, interview, and royalty fees alone far in excess of $1 million.~35 III.
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From page 355... ...
In May 2002 I spent three days at the AIM office in Palo Alto, reviewing the videotaped record of the 1996 Seattle conference. The following month I attended the Courant Institute workshop.
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From page 356... ...
Andrew Odlyzko: "It was said that whoever proved the Prime Number Theorem would attain immortality. Sure enough, both Hadamard and de la Vallee Poussin lived into their late nineties.
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From page 357... ...
With an excellent Italian meal under our belts and two hours of solid math talk behind us, having finally run out of things to ask, I said this: ID: Andrew, you have gazed on more non-trivial zeros of the Riemann zeta function than any person alive. What (lo you think about this darn Hypothesis?
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From page 358... ...
The rate of growth of S is so creepingly slow that the heights involved are beyond imagining; but certainly S will eventually get up to 100. lust how far would we have to explore up the critical line for S to be that big?
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From page 359... ...
I had better unmask myself at this point as a pure mathematician sans melange, having no interest in such questions at all. Most mathematicians and most theoretical physicists, too are motivated not by any thought of advancing the health or convenience of the human race, but by the sheer joy of discovery and the challenge of tackling difficult problems.
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From page 360... ...
Ways to test a large number for primality, ways to resolve large numbers into their prime factors, ways to manufacture gigantic primes; these all became very practical matters indeed in the last two decades of the twentieth century. Theoretical results, including some of Hardy's, were essential in these developments, which, among other things, allow you to use your credit card to order goods over the internet.
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From page 361... ...
In fact, Russell's work eventually brought forth Principia Mathematica, a key development in the modern study of the foundations of mathematics. Among the fruits of that study have been, so far, victory in World War II (or at any rate, victory at a lower cost than would otherwise have been possible)
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