A Quote by David Hilbert

Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure.
I realized that anything to do with Fermat's Last Theorem generates too much interest.
Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. Fermat's Last Theorem is the most beautiful example of this.
We are on the verge: Today our program proved Fermat's next-to-last theorem.
If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.
Too much knowledge could be a bad thing. I was lead to the Szemerédi theorem by proving a result, about squares, that Euler had already proven, and I relied on an "obvious" fact, about arithmetical progressions, that was unproved at the time. But that lead me to try and prove that formerly unproved statement- about arithmetical progressions-and that ultimately lead to the Szemerédi Theorem.
The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.
If something's important enough, you should try. Even if you - the probable outcome is failure.
If something's important enough, you should try. Even if - the probable outcome is failure.
I think I was just trying to coast and you can't coast and try and win at the same time, you know? It'll be three years now since those wins, but the last couple of years I've just really been trying to put my miles in, get them up there to 80 miles a week, 90 miles a week and put the work in again.
[Attributing the origin of life to spontaneous generation.] However improbable we regard this event, it will almost certainly happen at least once.... The time... is of the order of two billion years.... Given so much time, the "impossible" becomes possible, the possible probable, and the probable virtually certain. One only has to wait: time itself performs the miracles.
Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.
The three discrete invariances - reflection invariance, charge conjugation invariance, and time reversal invariance - are connected by an important theorem called the CPT theorem.
Even if I have only ten more years in front of me, it's such an intensive life. I have the feeling that I have already lived three lives in three years.
I loved doing problems in school. I'd take them home and make up new ones of my own. But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem - Fermat's Last Theorem.
Don't fear failure so much that you refuse to try new things. The saddest summary of a life contains three descriptions: could have, might have, and should have.
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