Good documentary about the proving of Fermat’s Last Theorem. (1 of 5) via **ContraWagner**

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mathematics

Good documentary about the proving of Fermat’s Last Theorem. (1 of 5) via **ContraWagner**

The Ulam spiral. - Black pixels show prime numbers.

**"An infinitude of prime numbers exists, as demonstrated by Euclid around 300BC. .. Given the fact that there is an infinity of primes, it is natural to seek for patterns or irregularities in the distribution of primes… The occurrence of individual prime numbers among the natural numbers is (so far) unpredictable, even though there are laws (such as the prime number theorem and Bertrand’s postulate) that govern their average distribution. Leonhard Euler commented :**

"Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate."

In a 1975 lecture, Don Zagier commented:“There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision.” “

Higher Mathematics

via - mudwerks: yellowblog: tappy: florencio:Las matemáticas pueden crear tendencias suicidas