PDA

View Full Version : Goldbach Conjecture/Riemann Hypothesis/etc

Alan Shore
22-06-2004, 11:43 AM
Actually I've got a question, has anyone proven the Goldbach conjecture yet?

That is, that every even number >2 is the sum of two primes.

Rincewind
22-06-2004, 12:05 PM
Actually I've got a question, has anyone proven the Goldbach conjecture yet?

Schnirelman (1939) proved that every even number can be written as the sum of not more than 300,000 primes.

Pogorzelski claimed to have proved it in 1977 but his proof is not generally accepted.

I believe Faber & Faber offered a \$1,000,000 prize if someone could produce a proof my March 2002. The prize went unclaimed.

It has also been shown to be true for n < some bound. Olivera e Silva in Oct 2003 announced it has been shown for all n < 6 x 10^16.

This is the latest information I have. I haven't heard of it being proved since Oct 2003 so I suspect not. It would have made news since it was first proposed in 1742. In fact, given it's long history the probability it has been proved sometime in the last 8 months is not great.

Alan Shore
22-06-2004, 12:15 PM
Schnirelman (1939) proved that every even number can be written as the sum of not more than 300,000 primes.

Pogorzelski claimed to have proved it in 1977 but his proof is not generally accepted.

I believe Faber & Faber offered a \$1,000,000 prize if someone could produce a proof my March 2002. The prize went unclaimed.

It has also been shown to be true for n < some bound. Olivera e Silva in Oct 2003 announced it has been shown for all n < 6 x 10^16.

This is the latest information I have. I haven't heard of it being proved since Oct 2003 so I suspect not. It would have made news since it was first proposed in 1742. In fact, given it's long history the probability it has been proved sometime in the last 8 months is not great.

Ah I see. I didn't want to use an outdated example when I was writing that it doesn't follow anyone knows anything a priori about the conjecture. If it had been proven this would not have been the case. Therefore there's an epistemological barrier in knowing whether the conjecture is a necessary truth or not.

Rincewind
22-06-2004, 01:39 PM
Ah I see. I didn't want to use an outdated example when I was writing that it doesn't follow anyone knows anything a priori about the conjecture. If it had been proven this would not have been the case. Therefore there's an epistemological barrier in knowing whether the conjecture is a necessary truth or not.

Fear not. For the purpose of the problem I posted, you can assume Goldbach's Conjecture to be true. That problem again...

The first snow of the season begins to fall during the night. The depth of the snow increases at a constant rate through the night and the following day. At 6 am a snowplough begins to clear the road of snow. The speed of the snowplough is inversely proportional to the depth of snow. In the period from 6 am to 8 am the snowplough clears 1 kilometer of road, but it takes a further 3.5 hours to clear the next kilometer.

At what time did it begin snowing?

arosar
16-07-2004, 02:36 PM
Oh my God!! Baz!! Did you hear mate? The Riemann has been solved . . .

But . . .

AR

Rincewind
16-07-2004, 04:32 PM
Oh my God!! Baz!! Did you hear mate? The Riemann has been solved . . .

But . . .

There was a media beat up around six weeks ago based on the following press release (http://news.uns.purdue.edu/UNS/html4ever/2004/040608.DeBranges.Riemann.html). They could talk the talk but seemed to fall down when trying to walk the walk.

Are you referring to this, or have there been new developments?

arosar
16-07-2004, 05:45 PM
Yes, that's what I was talking about. Heard it on the BBC last night. Apparently, this French bloke solved it. But problem for him is that none of his peers believe him and they won't read his work! He did solve some other, though less prominent problem, before.

AR

Rincewind
17-07-2004, 01:31 AM
Yes, that's what I was talking about. Heard it on the BBC last night. Apparently, this French bloke solved it. But problem for him is that none of his peers believe him and they won't read his work! He did solve some other, though less prominent problem, before.

"This French bloke" is Louis de Branges who is a Professor of Mathematics at Purdue. When the work is submitted for peer review it will no doubt be scrutinised by other mathematical academics. I don't know enough on the subject to give too much comment except that de Branges has been in the game a long time. In the 50's and 60's he proposed an approach to proving the Riemann. However, various problems with his proposal have been commented on later (Lax and Phillips, 1976) and even counter-examples questioning this approach have been identified (Conrey and Li, 1998).

As far as I'm aware these difficulties have not been addressed by de Branges so the mathematical community is for the moment taking his "internet published" proof with a grain of salt. No doubt should it be valid then this will come out in the wash of peer review. Proving Riemann is too big a thing to go unnoticed, however until such time as it is formally presented for review, a health dose of skepticism won't go astray.

Unfortunately, most popular science tele-magazine style programs ether don't understand this or believe it doesn't make for "good" copy (which is true). I believe the editors of these shows have an ethical responsibility to prefer content over form. However, I accept that holding this view may place me in the minority.

Note that I'm not saying de Branges doesn't have a proof, it may turn out that he has. However, current practice is not to report something as science (or even mathematics ;) ) which has not been peer reviewed. Remembering that the internet allows information to be propogated as quickly as misinformation.

If the impression you received from this story on the BBC was that this guy has a proof and academia was ignoring him unfairly (perhaps the old global conspiracy of academics) then that would seem to me to be a very dangerous way of representing the facts.

PHAT
17-07-2004, 06:50 AM
The first snow of the season begins to fall during the night. The depth of the snow increases at a constant rate through the night and the following day. At 6 am a snowplough begins to clear the road of snow. The speed of the snowplough is inversely proportional to the depth of snow. In the period from 6 am to 8 am the snowplough clears 1 kilometer of road, but it takes a further 3.5 hours to clear the next kilometer.

At what time did it begin snowing?

Hmmm, at first blush, this looks like a convoluted question that can be solved by calculus. I might have a scratch at this one. :uhoh:

Rincewind
17-07-2004, 11:38 AM
Hmmm, at first blush, this looks like a convoluted question that can be solved by calculus. I might have a scratch at this one. :uhoh:

Feel free, this should be discussed in the rec math thread. But don't read that one too closely as the answer has already been posted there. ;)

The current puzzle is the handshake problem (http://chesschat.org/showpost.php?p=21088&postcount=149).

Rincewind
04-04-2005, 02:45 PM
Interesting article on the use of computers in mathematics.

http://www.economist.com/science/displayStory.cfm?story_id=3809661

ursogr8
04-04-2005, 05:48 PM
^
Thanks Baz
Gave me a few ideas for my next 'discussion' with Bill. ;)
But it was short on ideas on how to respond to a/c or noidea.

Btw, I now yield on the QED, after reading the article.

tks
starter