Re: What would be the most important Mathematical discovery of all time?

Hi there Shawn!

It would appear your question got lost somewhere in the Great Inbox Shuffle of the Universe, and 
has landed in mine.

The two questions you pose are two very different questions.  The most important discovery in 
mathematics and the most important "completed equation" (whereby I'm going to make the 
assumption you might mean "completed proof" or something like it) of all time are two completely 
different things.

For the former, I'd posit that one of the most important discovery of all time might be the concept 
of zero, in that without it, little else would have come to pass.  

From there -- discoveries including great equations, concepts, identities and proofs -- I'd go with:

1) FFT (Fast Fourier Transform)
2) Euler's Identity
3) Fermat's Last Theorems

In terms of cornerstones of all things mathematical that changed the world -- Euclid's "Elements", 
without which we wouldn't be where we are today.  Also, the invention of Calculus, which changed 
the entire mathematical landscape.  And, for a more modern taste of things?  Public Key Encryption.

Hope this helps!  Mathematics are at the foundation of all things...  it's hard to pull out one thing 
and say "aha!  Here is what changed EVERYTHING for mankind!"  But if I had to identify one, single 
discovery?  I'd have to pick the discovery of "zero".

Be well, and keep on mathematizing,

MH