# Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group? [closed]

Why is there a deep mysterious relation between string theory and number theory (Langlands program), elliptic curves, modular functions, the exceptional group $E_8$, and the Monster group as in Monstrous Moonshine?

Surely it's not just a coincidence in the Platonic world of mathematics.

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At least this question is a bit childish. If anybody had an answer to this, he would publish it with a lot of "celebrations", and we all would know "why", in principle at least. – Georg Feb 7 '11 at 14:48
There are lots of interesting and appropriate questions involving these topics but this broad "why" question is not going to get any kind of reasonable answer. I'd suggest you reword the question to make it a more specific question about some aspect of these relations that you are interested in. – pho Feb 7 '11 at 15:10
I actually voted this question thumbs-up. It's a good question and I would like to know the most accurate answer, too. Clearly, the rough sketch of the answer is that string theory just knows about all important and exceptional structures in mathematics. But why does it know them? What is the logic that dictates that "other solutions" of a theory whose main physical goal is "only" to unify the interactions including gravity with quantum mechanics produces all other maths, including maths we used to think was totally abstract? Why did you close this very good question? – Luboš Motl Feb 8 '11 at 6:37
I agree with Luboš, the question should remain open. "Arduous" could also try asking at Math Overflow. (P.S. some of the specific connections listed come from the "modular invariance" of string theory, the need for one-loop amplitudes to be invariant under "large" reparametrizations of the world-sheet. This means that modular forms and their properties are relevant - thus Langlands - and also establishes a link to lattices - mathoverflow.net/questions/24604/… ) – Mitchell Porter Feb 8 '11 at 7:54
I still think a more specific question would be better, but I can see that there might be some interesting and useful answers so I've voted to reopen. – pho Feb 8 '11 at 14:20