Were Poincaré's leaps in proofs ever proven to be false?

  • Thread starter robertjford80
  • Start date
  • Tags
    Poincare
In summary: He had to invent geometric ways to handle the infinite sums before he could bring Riemann's ideas to the English speaking world.In summary, Poincare was known for his unconventional and intuitive approach to mathematics, often making large leaps in his proofs that left other mathematicians perplexed. While it is possible that some of his leaps may have later been proven to be false, there is no evidence to suggest that his overall reputation has been diminished. His untimely death may have prevented him from receiving the recognition he deserved, and he is still highly regarded in the mathematical community. Other mathematicians, such as P.S. LaPlace, were known for omitting details in their work, making it difficult for others to follow their ideas
  • #1
robertjford80
388
0
According to the experts, Poincaré made huge leaps in his proofs, often leaving lesser mathematicians scratching their heads. I'm wondering if some of those leaps later turned out to be false and if so how often.
 
Mathematics news on Phys.org
  • #2
It's not clear which experts you are relying on for this opinion about Poincare, nor do you cite any sources for these opinions.

http://en.wikipedia.org/wiki/Henri_Poincaré

Poincare was, by all accounts, not one to be overly bound by the logical underpinnings of mathematics. Unlike Frege or Bertrand Russell, he strongly disagreed that mathematics was a branch of logic, and he took a more intuitive approach in his mathematical researches.
 
  • #3
SteamKing said:
It's not clear which experts you are relying on for this opinion about Poincare, nor do you cite any sources for these opinions.

http://en.wikipedia.org/wiki/Henri_Poincaré

Poincare was, by all accounts, not one to be overly bound by the logical underpinnings of mathematics. Unlike Frege or Bertrand Russell, he strongly disagreed that mathematics was a branch of logic, and he took a more intuitive approach in his mathematical researches.

Fine, June Barrow-Green which can be found here:

http://www.bbc.co.uk/programmes/p0038x8l

It's toward the last five minutes of the program. I didn't think anyone would bother disputing it so obviously no need to back up sources. I still am wondering if his big leaps were later proved false.
 
  • #4
robertjford80 said:
I still am wondering if his big leaps were later proved false.

Not being familiar with the complete works of Poincare I cannot say that every one of his works is completely error free. In fact, it would be miraculous if Poincare managed to avoid making any blunders! I can say, however, that a good portion of the techniques he invented are still utilized (in some form or another) today.
 
  • #5
At PF, the more sources you provide, the better discussion you will obtain.

June Barrow-Green throws in a brief aside comparing Perelman with Poincare in the last few seconds of the program, specifically about how the two men's proofs allegedly contain gaps which are hard for lesser mortals to follow.

If you are looking for tabloid-like headlines which say "French mathematician's proof goes poof!", I don't think you'll find any. Poincare's reputation AFAIK remains undiminished a century after his death, and I know of nothing in his work which has been disproven. He was in many respects, a man ahead of his time, and in some fields like relativity, his work predates that of Einstein. IMO, his untimely death robbed him of some of the recognition which might have made his name as widely known as Einstein's.

Some mathematicians, like P.S. LaPlace were notorious for omitting a lot of the details in their work. When Nathaniel Bowditch, no slouch when it came to mathematics, undertook to translate LaPlace's 'Celeste Mecanique' into English, he found that the work of the Frenchman was extremely abbreviated, although it took five volumes to print it in the original. Bowditch not only translated LaPlace's work, but he also decided to check all of LaPlace's mathematical derivations himself.

After some time was spent on his project, Bowditch remarked, "Whenever I meet in LaPlace with the words 'Thus it plainly appears', I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears."
 
  • #6
SteamKing said:
At PF, the more sources you provide, the better discussion you will obtain.
I apologize. You're right. I should have done that.


IMO, his untimely death robbed him of some of the recognition which might have made his name as widely known as Einstein's.
This is so true.

Some mathematicians, like P.S. LaPlace were notorious for omitting a lot of the details in their work. When Nathaniel Bowditch, no slouch when it came to mathematics, undertook to translate LaPlace's 'Celeste Mecanique' into English, he found that the work of the Frenchman was extremely abbreviated, although it took five volumes to print it in the original. Bowditch not only translated LaPlace's work, but he also decided to check all of LaPlace's mathematical derivations himself.

After some time was spent on his project, Bowditch remarked, "Whenever I meet in LaPlace with the words 'Thus it plainly appears', I am sure that hours, and perhaps days, of hard study will alone enable me to discover how it plainly appears."

This is great information. I really want to thank you SteamKing for being such a great source of information. I really appreciate these posts of yours. They are a real joy to read.
 
  • #7
You're quite welcome.
 
  • #8
SteamKing said:
Some mathematicians, like P.S. LaPlace were notorious for omitting a lot of the details in their work.

. . . Riemann, his paper on counting primes. Really tough to follow even for the expert, Edwards, to go through.
 

1. Did Poincaré have any major scientific failures?

Yes, Poincaré had several scientific failures throughout his career. Most notably, his attempts at developing a theory of gravitation and his work on the three-body problem were not successful.

2. How did Poincaré's failures impact his overall contributions to science?

Poincaré's failures did not diminish his overall contributions to science. In fact, his failed attempts at solving certain problems led him to develop new mathematical concepts and methods that greatly advanced the fields of mathematics and physics.

3. Did Poincaré learn from his failures?

Yes, Poincaré was known for his ability to learn from his failures and use them as stepping stones for future successes. He believed that failures were an essential part of the scientific process and that they could lead to new discoveries and breakthroughs.

4. How did Poincaré handle his failures?

Poincaré handled his failures with a positive attitude and persistence. He would often continue to work on a problem even after experiencing multiple failures, and would approach it from different angles until he found a solution.

5. Are Poincaré's failures still relevant to modern science?

Yes, Poincaré's failures are still relevant to modern science as they have paved the way for new developments in mathematics and physics. His work on the three-body problem, for example, laid the foundation for chaos theory, which has numerous applications in modern science and technology.

Similar threads

Replies
33
Views
5K
  • General Discussion
Replies
3
Views
580
Replies
6
Views
821
  • Special and General Relativity
3
Replies
71
Views
15K
  • Special and General Relativity
Replies
5
Views
898
Replies
4
Views
911
  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
4
Views
987
  • Art, Music, History, and Linguistics
Replies
2
Views
811
Replies
1
Views
2K
Back
Top