What you’re going to read are mostly quoted from The Mathematical Universe and what I feel every time I read this piece of writings. If you interested, read this…
We’ll talking about one of Leonhard Euler’s discoveries concerned amicable numbers, a concept dating back to ancient times. It was the Greeks who defined two whole to be amicable if each was the sum of the proper divisors of the other. The number 220 and 284 are an example. That is, the divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, and, of course, 220. Discarding the last, we find that the sum of the proper divisors of 220 is
1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284
On the other hand, upon adding the proper divisors of 284, we get
1 + 2 + 4 + 71 + 142 = 220
Thus 220 and 284 are an amicable pair.
For many centuries this way the only known example of amicable numbers. The next breakthrough came from the thirteenth-century Arabic mathematician ibn al-Banna, who discovered the considerably more complicated pair 17,296 and 18,416. In 1636 the French mathematician Pierre de Fermat rediscovered al-Banna’s numbers and seemed quite pleased with this achievement. But in 1638, feeling somewhat less than amicable, his fierce rival Rene Descartes boasted about having found the even more stupendous pair 9,396,584 and 9,437,056. In the slang of today, the message from Descartes to Fermat was. "In your face!".
No further progress was made until Leonhard Euler came along in the eighteenth century. We stress that, at this point, only three sets of amicable pairs were known: those of Greeks, al-Banna, and Descartes. Euler took a deep breath, went to work, and produced nearly 60 additional pairs. In your face, Descartes!
Of course, what Euler did was to perceive a hitherto unrecognized pattern that allowed him to generate amicable numbers by the bushel. Leonhard Euler could examine an age-old problem and see something that had escaped the finest minds of previous generations.
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Euler took a deep breath, went to work, and produced nearly 60 additional pairs. In your face, Descartes!
First time I read and every time I remembered this sentence, I laughed, it’s really funny, funnier than most of the jokes i’ve ever read. This is something that made me laugh, awe and shiver in the same time. Hey.. but thats just me… if you don’t understand why… maybe I’m just another weirdo for you