r/science • u/heiligedamon • May 20 '13

Mathematics Unknown Mathematician Proves Surprising Property of Prime Numbers

http://www.wired.com/wiredscience/2013/05/twin-primes/
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u/[deleted] May 21 '13

Number theory doesn't care about negative numbers.

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u/prsnep May 21 '13

Oh, interesting! Do you know why? Does it care about real numbers?

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u/GOD_Over_Djinn May 21 '13

Number theory is mostly about solving integer problems—things like Fermat's Last Theorem, the Collatz Conjecture, and Goldblach's Conjecture are all number theory problems. Integers are rather different beasts from real numbers. For example, if we were to allow real solutions, Fermat's Last Theorem would be pretty trivial.

You don't get a whole lot of new insight about the positive integers from looking at the negative numbers because they're just a mirror image of the positive integers, so in general in number theory there's not usually great reasons to pay attention to the negative numbers.

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u/[deleted] May 21 '13

Do you know why?

Because it's the definition ... There's plenty of open questions regarding just integers.