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HalfThere wrote:I would guess that a grad in math, maybe a PHD, would probably be able to do it, but maybe you're right.
Where would I be able to find a place with people who have such mastery of modern mathematics as you think are needed to weigh this question?
Gaydar2000SE wrote:I just hate Wiles because he did it for the glory with his working in secrecy business, serves him right that he erred on the first go.
Also, I share Perelman's idea that it should be about the results and not about the people. Also, every mathematical theorem proven is essentially built upon other theorems, lemmata and otherwise, surely then the contribution is vast, the one who lays the last block just gets the prize? I mean, what if Wiles first proved that elliptic curve thing, forgot how it was called. And then some other person came with 'Yeah, but if fermat's is true, then some elliptic curves aren't modular, didn't some guy 50 years back prove that ALL elliptic curves are?', would they then posthumously award Wiles the Fields and the Millennium and what-not? It's just a matter of subjection who has done the most important part. I mean, obviously the most important thing was the guy who invented the concept of axiomatic proving, shouldn't he get ALL the awards?
Well, I know a mathematician would have to be under 40 for the Fields, also I think it to be conceivable that if it wasn't proven by then Fermat would be in the Millennium Prizes no? I was referring to that, Wiles actually formulated a specification for the Prizes, they were made after he got to the front for Fermat, I know this.auteur52 wrote:Gaydar2000SE wrote:I just hate Wiles because he did it for the glory with his working in secrecy business, serves him right that he erred on the first go.
Also, I share Perelman's idea that it should be about the results and not about the people. Also, every mathematical theorem proven is essentially built upon other theorems, lemmata and otherwise, surely then the contribution is vast, the one who lays the last block just gets the prize? I mean, what if Wiles first proved that elliptic curve thing, forgot how it was called. And then some other person came with 'Yeah, but if fermat's is true, then some elliptic curves aren't modular, didn't some guy 50 years back prove that ALL elliptic curves are?', would they then posthumously award Wiles the Fields and the Millennium and what-not? It's just a matter of subjection who has done the most important part. I mean, obviously the most important thing was the guy who invented the concept of axiomatic proving, shouldn't he get ALL the awards?
Let's get a few things straight. Wiles did not win the Millennium Prize, it was not offered for Fermat. Wiles did not win the Fields Medal, as he was too old. Also, the other people who made substantial contributions (Ribet, Frey, Taylor, Serre, to name just a few) have had their own share of glory and are mostly household names for mathematicians. Sure, there may not have been an article about them in the New York Times, but I highly doubt that was Wiles's motivation.
Gaydar2000SE wrote:That theorems and laws are named after people is also really just a sign of human lust for glory and popularity.
Newton's first law <=> The Law of equality of force to the derivative of momentum to time., or shorter: The Law momentum and forceauteur52 wrote:Gaydar2000SE wrote:That theorems and laws are named after people is also really just a sign of human lust for glory and popularity.
How do you figure? Wouldn't it make more sense that we are just trying to honor people that we respect? People do not (usually) name theorems and definitions after themselves.
Edit: Plus the fact that there are only so many words to describe things. If we didn't name things after people, we would have a hard time coming up with so many snappy names.
Gaydar2000SE wrote:I mean, what if Wiles first proved that elliptic curve thing, forgot how it was called. And then some other person came with 'Yeah, but if fermat's is true, then some elliptic curves aren't modular, didn't some guy 50 years back prove that ALL elliptic curves are?', would they then posthumously award Wiles the Fields and the Millennium and what-not? It's just a matter of subjection who has done the most important part.
Gaydar2000SE wrote:That Leibniz and Newton battle about who invented calculus is also sickening, come on, all that matters is that it's there, especially because both of them divided by zero. They just called it 'the infinitesimal'
Gaydar2000SE wrote:The prime number theorem' and 'The main theorem of arithmetic', neither are named after Euclid which proved them.
Gaydar2000SE wrote:Euclid essentially gave a proof that was not completely rigorous to them by today's standards. Though note that today's rigour has it's roots in only a 100 years back
Gaydar2000SE wrote:essentially nothing Euler or Newton did was the mathematical rigour they ask of undergraduate students today. Newton divided by zero quite a lot.
Pietro wrote:(he is "everywhere dense" in mathematics)
Ease of communication? How's saying 'Newton's fist law of motion' any easier than 'The Law of momentum-and-force'? The latter is surely quite a lot more descriptive, strangely. 'Euclid's theorem' is a lot shorter than 'The fundamental theorem of arithmetic' and both are equally vague in name. Naming theorems after people essentially causes confusion if people had more than one interesting result. The 3 and the 1 are quite arbitrary of course in Newton's case.dissonant wrote:Man, you need to relax. We name theorems after people for a lot of reasons. Respect is a big part of it. But a lot of the time it is just for ease of communication. I really can't think of a snappy name for Green's Theorem for instance. But I would immediately understand what you meant if you said it.
I never said it was the only part, I said it mattered to him that he was the one that proved it. Not that it was proven in the end by some one. Your sentence seems to imply we agree here. Typical really, one sees it every where, vegetarians do not care for that meat isn't eaten, they care for it that they aren't the ones that eat it. I have it too, I find it a lot worse if for instance a friend of mine cries and I was the one that caused it, it's disgusting, that said cries is all that matters, not who caused it, the damage is done and that I was the one that caused it isn't relevant. Truly disgusting aspect of people here. And in the end we all try to delude ourselves that we're caring to heal it.To say Wiles proved Fermat's Last Theorem only for the glory seems completely unfounded. I have read that he came across the theorem in his youth, it was obviously a personal obsession of his. It seems naive to say that he was only in it for the fame, although I am sure that was a part of it.
True, ahaha. Poor guy though, he retired from maths after that, the pictures taken of him in the trains and all, ahah, he's apparently scared to go out of (his mother's) house.Also, Perelman is surely much more famous for rejecting his Field's medal rather than accepting it.
Newton quite did divide by zero to produce his derivatives and his methodology often returned simply absurd errors and the approach was then to simply go another path until it's no longer absurd. Derivative functions in the days of Leibniz and Newton were never rigorous mathematics, in fact, the concept didn't even exist really then as it was never quite clearly stated what axioms are used. They used naïve imported explicitly and implicitly axioms they saw around them and deemed 'common sense'. There was no definition of what 'real numbers' really were back then but Newton used the standard addition and added a certain constant p a lot to a given x to leave x. That's an additive identity per definition, and where he operated the additive identity is the only element that does not have a multiplicative inverse. Yet he still divided by that p a lot of times to make his derivatives. That p is often just called 0, in Newton's day people had the idea that it was a different object, often called such things as 'the smallest possible thing next to zero' or 'infinitely small', real numbers are dense, there is no 'smallest possible next to zero', if there is no other element between p and 0 then p = 0.Newton never talked about infinitesimals; he focused on the concept of derivative, which he called "fluxions". In the Principia, he doesn't even use these; it's all Euclidean geometry and limiting arguments. There is not a single mathematical gap in the first book of the Principia (which is the more mathematical part). Even in his other, more liberal work on infinite series, saying he "divided by zero" is a gross misrepresentation of the semi-formal arguments he presented, and anachronistic to the point of irrelevance.
Euclid proved that there is not a finite number of primes, and his proof stands perfectly today. This is not what is called the "Prime Number Theorem".
Find me a few example of his graph theory that has problems, then. I want specific examples, not hand waving.Gaydar2000SE wrote:Euler's lack of rigour is far deeper, in fact, it's essentially what filled the entirety of mathematics until Russell tore it all down, the point is that Euler never was explicit about what axioms precisely he proved from. And a lot of axioms in those days were implicitly assumed because they just 'made sense' to the common naïve realist perception. There was really no hard way in that time to why one couldn't implicitly assume the theorem to prove to be true and then beg the question because from what axioms it was being proven was not set in stone. The only thing that stopped people was the subjective line of 'that it just didn't feel good', hardly mathematics of course.
Gaydar2000SE wrote:Ease of communication? How's saying 'Newton's fist law of motion' any easier than 'The Law of momentum-and-force'? The latter is surely quite a lot more descriptive, strangely.
Gaydar2000SE wrote:I know, I meant that Euclid gave a 'rough' proof of the fundamental theorem of arithmetic, the prime number theorem came quite some time later. Also, his prove doesn't stand, his conclusion stands. It was dumb luck actually. I could point out one flaw in his proof. To begin with his proof depends on the existence of a total order on the naturals and he didn't prove it was there. He just naïve assumed that if one has two natural numbers n,m, unequal, that one is larger than the other, he never proved it. It makes sense to human intuition, naïve mathematics opposed to axiomatic.
Token wrote:Gaydar2000SE wrote:I know, I meant that Euclid gave a 'rough' proof of the fundamental theorem of arithmetic, the prime number theorem came quite some time later. Also, his prove doesn't stand, his conclusion stands. It was dumb luck actually. I could point out one flaw in his proof. To begin with his proof depends on the existence of a total order on the naturals and he didn't prove it was there. He just naïve assumed that if one has two natural numbers n,m, unequal, that one is larger than the other, he never proved it. It makes sense to human intuition, naïve mathematics opposed to axiomatic.
You have a strange definition of "flaw".
Token wrote:Gaydar2000SE wrote:I know, I meant that Euclid gave a 'rough' proof of the fundamental theorem of arithmetic, the prime number theorem came quite some time later. Also, his prove doesn't stand, his conclusion stands. It was dumb luck actually. I could point out one flaw in his proof. To begin with his proof depends on the existence of a total order on the naturals and he didn't prove it was there. He just naïve assumed that if one has two natural numbers n,m, unequal, that one is larger than the other, he never proved it. It makes sense to human intuition, naïve mathematics opposed to axiomatic.
You have a strange definition of "flaw".
LE4dGOLEM wrote:your ability to tell things from things remains one of your skills.
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Gaydar2000SE wrote:I find the latter case much more descriptive, after all, it's called 'The prime number theorem' and 'The main theorem of arithmetic', neither are named after Euclid which proved them.
dissonant wrote:Man, you need to relax.
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