Friday, March 18, 2011

Happy Birthday, Christian

Today in 1690 Christian Goldbach was born, in Königsberg, part of Brandenburg-Prussia.

His famous conjecture:
Every even integer greater than 3 can be written as the sum of two primes
remains unproved (though intuitively obvious), but he's also remembered for the the Goldbach–Euler theorem (also known as Goldbach's theorem), which states that the sum of 1/(p − 1) over the set of perfect powers p, excluding 1 and omitting repetitions, converges to 1. (The perfect powers are 4, 8, 9, 16, 25, 27 - whole numbers which are other whole numbers raised to a power (squared, cubed, etc).) So the theorem is that 1/3 + 1/7 + 1/8 + 1/15 + 1/24 ... = 1.

Whoo! Math! It kills me, but I love it (abstractly).



At 6:03 AM, March 18, 2011 Blogger sara had this to say...

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At 1:13 AM, March 19, 2011 Anonymous Anonymous had this to say...

Of course, technically Goldbach's conjecture in its original form didn't say anything about "greater than 3". It's just that you need that clause in order to translate the conjecture into modern mathematical language.

In Goldbach's day, mathematicians had not yet settled on a definition of "prime" that excludes 1. After all, 1 has no factors other than 1 and itself. But it's unique in that 1 IS itself.


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