Um, unless I have a huge blind spot, the article says no such thing. In fact, this article makes it clear that the latest article he has published was in March 2003, and although a further paper is forthcoming, it is believed that the first two papers contain a correct proof.
As far as I can tell, it seems the fuss is rather about the distinguished mathematician (math popularizer, rather) Keith Devlin saying that he thinks it is correct... but as far as I can tell, he has no special authority on the problem and hasn't looked it over in the details
This review of Karl Sabbagh's book The Riemann Hypothesis contains some background on De Branges.
http://www.maa.org/reviews/sabbaghRH.html
He sounds like quite a character, from that and from his "apology"... given recent trends, I wonder if someone might write a novel or play about him?
I don't have the mathematical background to fully confirm this, but his "apology" paper looks like a sketch of a proof of the Riemann hypothesis. With all the details worked out, it would be a good bit longer. It appears that de Branges has published this in order to back up priority claims as needed, and the apology would be sufficient for such a purpose.
Tell that to Euclid! His Elements basically defined the notion of "proof" and although there were occasional gaps in rigor, it contains a good number of proofs. The main handicap the ancient Greeks had was not a lack of proofs, but a lack of notation (algebra didn't come along until the Arabs).
Okay, so chess is the newest 'sport' ocvered by ESPN. I saw the match on TV and was reasonably interested, however my favorite part was making fun of the commentators. I should give them their due -- they were professional chess players, and they had to keep people from changing the channel during Kasparov's 15-minute wait considering the rook sacrifice the commentators considered obvious.
I suppose it is to be expected that people commenting on a chess game being played on ESPN would make lame sports metaphors (though I was waiting for Kasparov to be compared to Tiger Woods) and feeble attempts at explaining the game to random channel-surfers "the ranks are the horizontal rows, the files are the vertical ones", but the whole speculation about whether the computers would come invade our living rooms after they had finished beating us at chess -- really! I was interested by Susan Polgar's cameo appearance on the show (though not a chess player I admire women who succeed in traditionally non-female fields) and the discussion of the impact on computers on the number of chess prodigies nowadays (computers don't worry about being humiliated by a 12 year old, making it easier for youngsters to find opponents -- or so they say).
Really, I'd like to see some computer really trounce all the humans out there so that we can get over this computer chess thing and on to something more serious.
Personally, this reminds me of the little green blobs on the covers of the Hitchhiker's Guide books.
Speaking of which, I tried Babelfish on that site and it told me of its "spatula contraction technology". Perhaps I am just not sufficiently geeky to understand that.
How long has this been going on?
on
Meet The Leonids
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· Score: 2, Insightful
It seems like every year since 1998 they've been predicting the best meteor shower ever. *jaded* Ah, it appears this will be the last one. Perhaps I will get up at 4AM again. I did it last year and it was really impressive -- even the view from our window was something.
10 megs? You must be kidding. I got it in 1998 and it only offered 3 megs at the time. Around 2000 they upped the space to 6 megs, which was nice. But I still wish they had better spam filtering, though. About a third of my spam doesn't get caught.
Depends upon what you mean by 'that'. I personally would be happier having Nader endorse Gore in a follow-up runoff election than just having him hand the votes over to Gore. It would also keep him from alienating those who support Nader but for some reason hate Gore (eg people who came to the Greens from the Republican party), neither of which would be thrilled with the idea that their votes would eventualy end up with Gore.
The political spectrum is not a well-defined line, and your proposal would be hard on candidates who do not fit easily into it. Certainly the Henry Clay example wouldn't happen now, but I still would be happier with giving the people more leeway to let their preferences be heard in a nontrivial election.
The idea of candidates personally trading the votes their voters bestowed on them seems rather sketchy and back-room. I can't help thinking of the historical election in the 1830's (?) where there were four candidates running and no majority in the electoral college, so the election went to the Senate. In the end Henry Clay dropped out of the election and traded his senatorial votes to Andrew Jackson in return for a position as Secretary of State. (Of course his defenders would have us believe there is no connection between the two events, but be realistic.)
Of course, Ralph Nader would never do that, but the situation could still lend itself to corruption.
As I recall, that program (or one designed for a similar goal) involved a great deal of 'prodding' from its programmers... e.g. telling it that 'even number' is an interesting concept, 'prime number' is an interesting concept, 'sum' is an interesting concept.
Not too surprising that it managed to discover Goldbach's conjecture that every even number can be expressed as a sum of two primes.
Is a computer program ever going to invent mathematics without previous knowledge of it just because it finds it to be a useful utility for solving problems?
Note that no single human person invented mathematics, and that the vast majority would be unable even to start. The invention of mathematics happened over tens of thousands of yeras among huge numbers of people. It is patently ridiculous to expect a single computer to match the achievements of a whole human culture. However this does not mean that one computer, in the context of society, could do as well or surpass the achievements of many humans.
Is the point here to educate kids or to sell videogames? Setting aside those rare good games (eg SimCity, The Incredible Machine), most games with pretentions to 'educationalness' are just flash cards dressed up with animation and other distracting excitement.
Though I do remember I owned MathBlaster Mystery when young, and it was a pretty good game, not in the cheesy animation way (it ran on our old DOS machine) but it had some pretty good logic-puzzle-ly games which also exercised math skills, one of them was like Mastermind meets multiplication (instead of a row of colored peg, you had to guess some two-digit muliplication problem).
I second that. (And while we're at it, how about 'e' for a nonsexist 3rd person pronoun?) However, I think 'u' for 'you' will be the limit of how far IM-speak will influence the spelling written English language (vocabulary is another matter -- abbreviations like brb and ttyl do have some use and are likely here to stay). True l33t is harder to read than normal language and is likely to be a passing fad that will die away within 10 years. Spellings such as b4 are just plain cheesy and will never make it into standard usage, and 'kewl' really isn't that much more phonetic than 'cool'...
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Um, unless I have a huge blind spot, the article says no such thing. In fact, this article makes it clear that the latest article he has published was in March 2003, and although a further paper is forthcoming, it is believed that the first two papers contain a correct proof.
As far as I can tell, it seems the fuss is rather about the distinguished mathematician (math popularizer, rather) Keith Devlin saying that he thinks it is correct... but as far as I can tell, he has no special authority on the problem and hasn't looked it over in the details
This review of Karl Sabbagh's book The Riemann Hypothesis contains some background on De Branges. http://www.maa.org/reviews/sabbaghRH.html He sounds like quite a character, from that and from his "apology"... given recent trends, I wonder if someone might write a novel or play about him?
Hm. It appears that I did not notice that the real proof is in fact here.
I don't have the mathematical background to fully confirm this, but his "apology" paper looks like a sketch of a proof of the Riemann hypothesis. With all the details worked out, it would be a good bit longer. It appears that de Branges has published this in order to back up priority claims as needed, and the apology would be sufficient for such a purpose.
Tell that to Euclid! His Elements basically defined the notion of "proof" and although there were occasional gaps in rigor, it contains a good number of proofs. The main handicap the ancient Greeks had was not a lack of proofs, but a lack of notation (algebra didn't come along until the Arabs).
Okay, so chess is the newest 'sport' ocvered by ESPN. I saw the match on TV and was reasonably interested, however my favorite part was making fun of the commentators. I should give them their due -- they were professional chess players, and they had to keep people from changing the channel during Kasparov's 15-minute wait considering the rook sacrifice the commentators considered obvious. I suppose it is to be expected that people commenting on a chess game being played on ESPN would make lame sports metaphors (though I was waiting for Kasparov to be compared to Tiger Woods) and feeble attempts at explaining the game to random channel-surfers "the ranks are the horizontal rows, the files are the vertical ones", but the whole speculation about whether the computers would come invade our living rooms after they had finished beating us at chess -- really! I was interested by Susan Polgar's cameo appearance on the show (though not a chess player I admire women who succeed in traditionally non-female fields) and the discussion of the impact on computers on the number of chess prodigies nowadays (computers don't worry about being humiliated by a 12 year old, making it easier for youngsters to find opponents -- or so they say). Really, I'd like to see some computer really trounce all the humans out there so that we can get over this computer chess thing and on to something more serious.
Personally, this reminds me of the little green blobs on the covers of the Hitchhiker's Guide books. Speaking of which, I tried Babelfish on that site and it told me of its "spatula contraction technology". Perhaps I am just not sufficiently geeky to understand that.
It seems like every year since 1998 they've been predicting the best meteor shower ever. *jaded* Ah, it appears this will be the last one. Perhaps I will get up at 4AM again. I did it last year and it was really impressive -- even the view from our window was something.
10 megs? You must be kidding. I got it in 1998 and it only offered 3 megs at the time. Around 2000 they upped the space to 6 megs, which was nice. But I still wish they had better spam filtering, though. About a third of my spam doesn't get caught.
Depends upon what you mean by 'that'. I personally would be happier having Nader endorse Gore in a follow-up runoff election than just having him hand the votes over to Gore. It would also keep him from alienating those who support Nader but for some reason hate Gore (eg people who came to the Greens from the Republican party), neither of which would be thrilled with the idea that their votes would eventualy end up with Gore. The political spectrum is not a well-defined line, and your proposal would be hard on candidates who do not fit easily into it. Certainly the Henry Clay example wouldn't happen now, but I still would be happier with giving the people more leeway to let their preferences be heard in a nontrivial election.
The idea of candidates personally trading the votes their voters bestowed on them seems rather sketchy and back-room. I can't help thinking of the historical election in the 1830's (?) where there were four candidates running and no majority in the electoral college, so the election went to the Senate. In the end Henry Clay dropped out of the election and traded his senatorial votes to Andrew Jackson in return for a position as Secretary of State. (Of course his defenders would have us believe there is no connection between the two events, but be realistic.) Of course, Ralph Nader would never do that, but the situation could still lend itself to corruption.
As I recall, that program (or one designed for a similar goal) involved a great deal of 'prodding' from its programmers... e.g. telling it that 'even number' is an interesting concept, 'prime number' is an interesting concept, 'sum' is an interesting concept. Not too surprising that it managed to discover Goldbach's conjecture that every even number can be expressed as a sum of two primes.
Is a computer program ever going to invent mathematics without previous knowledge of it just because it finds it to be a useful utility for solving problems? Note that no single human person invented mathematics, and that the vast majority would be unable even to start. The invention of mathematics happened over tens of thousands of yeras among huge numbers of people. It is patently ridiculous to expect a single computer to match the achievements of a whole human culture. However this does not mean that one computer, in the context of society, could do as well or surpass the achievements of many humans.
Is the point here to educate kids or to sell videogames? Setting aside those rare good games (eg SimCity, The Incredible Machine), most games with pretentions to 'educationalness' are just flash cards dressed up with animation and other distracting excitement. Though I do remember I owned MathBlaster Mystery when young, and it was a pretty good game, not in the cheesy animation way (it ran on our old DOS machine) but it had some pretty good logic-puzzle-ly games which also exercised math skills, one of them was like Mastermind meets multiplication (instead of a row of colored peg, you had to guess some two-digit muliplication problem).
I second that. (And while we're at it, how about 'e' for a nonsexist 3rd person pronoun?) However, I think 'u' for 'you' will be the limit of how far IM-speak will influence the spelling written English language (vocabulary is another matter -- abbreviations like brb and ttyl do have some use and are likely here to stay). True l33t is harder to read than normal language and is likely to be a passing fad that will die away within 10 years. Spellings such as b4 are just plain cheesy and will never make it into standard usage, and 'kewl' really isn't that much more phonetic than 'cool'...