Taniyama-Shimura conjecture (idea) by Spuunbenda

The claim that every elliptic curve is also a modular form in disguise.

Also called the Shimura-Taniyama-Wiles Conjecture, STW is an ambitious attempt to connect two apparently unrelated areas of mathematics: the theory of numbers and the theory of shapes.

I find amusing one commentator's attempt to clarify this mindbendingly esoteric topic:

"Only front-line mathematicians will really understand the STW conjecture. But you could say 'there exists a modular form of weight two and level N which is an Eigenform under the Hecke series and has a Fourier series.'"

STW was used by Andrew Wiles as part of his 1993 proof of Fermat's Last Theorem.

Congratulations, you have eliminated all forms of hospitable life	Fermat's Last Theorem	elliptic curve	Andrew Wiles
The difficulties of a modular computer	Superstring Theory	Fermat will never find solace of yes	Taniyama
I just spent $175.00 on black silk underwear	Poincaré Conjecture	algebraic geometry	Shin Megami Tensei
Fourier series	Advanced Dungeons and Dragons	Pierre de Fermat	number theory
modular function	Catalan's conjecture	Slashdot trolling as an art form	yukata
Lives of the mathematicians	torus	String Theory	Gaussian prime