![]() ![]() At that point the hard reality of numbers kicks in with all its might, may it be Platonic, Realistic, or just Mathematical. Even the most anti-scientific philosopher can be silenced with ease by a suitable application of rituals and theories of social truth to the number that is written on his paycheck. Nobody asks whether numbers are just a ritual, or at least not very many mathematicians do. I was not going to write anything, as I am a latecomer to this masterful troll question and not many are likely going to scroll all the way down, but Paul Taylor's call for Proof mining and Realizability (or Realisability as the Queen would write it) was irresistible. (emphasis added by YC to the earlier post) It would be more interesting to have an example of a false statement which was accepted for many years but I can't provide an example. When the error was pointed out, there was again a gap of many years before a correct proof was constructed, using methods that Dehn never considered. This is a true statement, with a false proof that was accepted for many years. All the insight in the world can't replace it. The final test is certainly to have a solid proof. There is a problem in deciding what level of detail is necessary for a convincing proof-but that is very much a matter of taste. Some mathematicians are great at insight but bad at organization, while some have no original ideas, but can play a valuable role by carefully organizing convincing proofs. The next step is a careful attempt to organise the ideas in order to convince others. Mathematical thought often proceeds from a confused search for what is true to a valid insight into the correct answer. Here is his "impromptu answer to the question" (this is his exact words with his permission): "it seems very unlikely that I said that.". ![]() I have checked the "quote" referred to him with him and he wrote Update: The very well-known mathematician who I mentioned above is John Milnor. However, I learned what kind of question I cannot ask! It was four in the morning that I came to MO, hoping to find something to relax myself, finding the truth perhaps. I knew there were (are) people who put their lives on the line to gain rigor. "Philosophical breakdown" (see above) was the exact term he used, "quoting" a very well-known mathematician. But, the greatest attack came from one of the audience, graduated from Princeton and a well-established mathematician around. I was aware of the "strange" ideas of one of the panelist. That afternoon, I came back late and I couldn't go to sleep for the things that I had heard. Reaction: Here I try to explain the circumstances leading me to ask such "odd" question. Do mathematicians not preach what they practice (or ought to practice)? I am indeed puzzled! ![]() To my great surprise and shock, I should convince my mathematician colleagues that proof is indeed important, that it is not just one ritual, and so on. I was in a funny and difficult situation. ![]() What I was hearing was "death to Euclid", "mathematics is on the edge of a philosophical breakdown since there are different ways of convincing and journals only accept one way, that is, proof", "what about insight", and so on. Yet, I am a mathematics educator who was one of the panelists of a discussion on "proof" this afternoon, alongside two of my mathematician colleagues, and in front of about 100 people, mostly mathematicians, or students of mathematics. That was my answer till this afternoon! "Mathematics without proofs isn't really mathematics at all" probably was my longer answer. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |