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robertjford80
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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.
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.
robertjford80 said:I still am wondering if his big leaps were later proved false.
I apologize. You're right. I should have done that.SteamKing said:At PF, the more sources you provide, the better discussion you will obtain.
This is so true.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."
SteamKing said:Some mathematicians, like P.S. LaPlace were notorious for omitting a lot of the details in their work.
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.
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.
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.
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.
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.