20 years. Wow. 20 years before my Ph.D. we didn't have a P vs. NP problem. Does the PCP theorem seem as ancient to today's grad students as Cook's theorem was to me?
In those 20 years we had incredible advances in
- Complexity of approximations which includes developments of interactive proofs, probabilistically checkable proofs, the parallel repetition theorem, semi-definite programs, and unique games.
- Great advances in coding theory in particular list-decoding codes.
- Tight connections between circuit hardness and derandomization. And we don't need random coins anymore for primality.
- Explicit constructions of extractors, expanders and various other combinatorial objects with SL=L coming out of this theory.
- Quantum computing.
- Proof Complexity.
- Cryptography. Almost anything you can imagine you can implement cryptographically, at least in theory.
- The applications of computation theory to economic theory and vice versa.
- Amazing connections between all of the above.
I've seen the Internet go from E-mail to Twitter. I've seen fax machines and CDs go from amazing technologies to has beens. And computers got much faster and smaller. I no longer have time for a restroom break when I LaTeX a paper.
Technology that hasn't changed much: Transportation. I still get from point A to point B the same way I did twenty years ago though now without being fed.
What will the next twenty years bring? Many great theorems. Definitely. Multi-core computers with millions of cores. Probably. Large-scale quantum computers. Doubtful. A proof that P≠NP. Don't count on it.