On Sat, Nov 20, 2010 at 9:51 PM, rjf <fate...@gmail.com> wrote: > > > On Nov 20, 4:49 pm, kstueve <kevin.stu...@gmail.com> wrote: > >> >> One of the reasons making the fastest possible pi(x) available is >> important is because of its relationship to the Riemann hypothesis. A >> proof of the Riemann hypothesis would not only provide immense insight >> into areas of mathematics as diverse as arithmetic and complex >> analysis, it would also provide great insight into the relationship >> between order and randomness in mathematics, and possibly even shed >> light on the role of randomness in the collapse of the wave function >> in quantum mechanics. > > Really? If an alien landed in a flying saucer and told you the answer > to > this conjecture, what insight would it give you that is different from > (say) > assuming a particular result, and proceeding from there ? > > It seems to me you can do all the supposing and figuring the > consequences right now, > simply by taking two independent paths. As many have done.
He's talking about the insight that a _proof_ could yield, not the insight that one gets simply by knowing that the conjecture is true. These are entirely different things. Obviously, one has to be mathematically sophisticated enough to know what a proof is to understand that. > Also, why do you expect that computing values of pi(x) would provide > any > further insight into this matter? Do you think that the distribution > of primes > takes off in a different direction after N=10 trillion? > > Now it may be that the original poster is an excellent math student > and > programmer, but it seems that he's taken almost no math courses, > judging by the subjects he has NOT studied. We are told nothing > about his computer science background either. So maybe it doesn't > matter if he pursues a pointless project and learns almost nothing > about > the use of parallelism in contemporary scientific computing. He absolutely didn't ask about the use of "parallelism in contemporary scientific computing". He asked for a senior undergrad project "involving programing, algorithms, parallel processing, and mathematics [...] that could be developed or needs to be developed for the sage community." > Studying the Riemann hypothesis may be a fun challenge, or > for trying to earn the Clay institute prize, but beyond that, is > knowing the truth going to have any effect outside of pure math? > > Just asking. > > RJF The only way to know would be to be omniscient. Even if a proof of RH were found tomorrow, and 2 years from now there are no publicly known applications outside of pure math, that doesn't prove an application won't be found 30 years from now, or 300 years from now. What we can be certain of is that if we don't encourage young people today to think about deep problems, they probably won't. There is also a long history of results in so called "pure mathematics" turning out to be very useful, sometimes long after the original discoverer is gone. But asking a mathematician to care about such things is somewhat like asking your daughter about applications of her music [1] to Physics -- she probably wouldn't care, even if there were applications. -- William [1] http://en.wikipedia.org/wiki/Johanna_Fateman -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
