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 primesremains 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).
Labels: birthdays
1 Comments:
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At 1:13 AM, March 19, 2011
Anonymous had this to say...
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<-- Older Post ^ Home Newer Post -->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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