This is the first post of 2016! (that is not a factorial). Hence I will make some predictions and at the end of the year I'll see how I did
1) The USA Prez election will have two main candidates: Hillary Clinton and Ted Cruz. Clinton will win by floating rumors that Cruz was born in a foreign country.
2) There will be a proof that there exists a constant c such that the methods that got a lower bound of (3+1/86)n on an explicit function cannot be extended to cn.
3) P vs NP will not be solved. But see next point.
4) I will be asked to look at at least two resolutions of P vs NP. This year I was asked to look at two
proofs that P=NP. Neither was correct.
5) GI will still not be in known to be in P.
6) There will be a proof that Babai's techniques cannot get GI into P.
7) The fact that 2016=25327 will be useful in a math competition.
8) Posting a video of a talk (as Babai did) will become an acceptable way to claim a result, rather than having a paper on arXiv. Getting a paper in a Journal will become less and less relevant for big results.
(This is a topic for a later blog post.)
9) The Unique Game conjecture... When it was first stated it seemed like maybe it could be proven or disproven. The longer it stays open the harder it seems. Clyde Kruskal tells me that a good method for guessing how long a problem will stay open is how long its been open. So I'll predict it won't be resolved this year. However, by that reasoning, I will always predict it will not be resolved in the following year.
10) There will be a big data breach. The security protocols used were never proven secure, though that won't be what caused the breach. Nor was it caused because of a really fast factoring or DL algorithm.
11) Comp Sci enrollment will continue to rise.
12) Leave your predictions in the comments!