I realize that 99% of mathematicians are in the “the new decade doesn’t begin until 2011″ camp, but I started wondering, how does mathematics look different now than it did in 2000? The big news of the decade was the solution of the Poincaré conjecture and more generally the geometrization conjecture. At the time, I remember hearing it widely predicted that this spelled doom for the topic of 3-manifolds. Is that what really happened?
Also, while progress in certain areas, such as algebraic geometry, algebraic topology, and number theory are high profile, what’s happened in the rest of mathematics? Graph theory saw the proof of the graph minor theorem (which I remember being earlier, but Wikipedia claims was only completed in 2004), but I don’t know what else happened in the area. Were there any major new breakthroughs, or changes in perspective in group theory? Logic? Universal algebra? Game theory?
In a related note, the proof of a conjecture known as the Fundamental Lemma made Time magazine’s list of the top scientific discoveries of 2009.
But 100% of computer scientists zero-index and call this a new decade. I’m surprised you think so many mathematicians disagree.
In logic as far as I know the major change in perspective is in becoming more “applied”. I.e. most of the stuff I heard is at least somehow related to getting algorithms for certain problems.
stolee: Just anecdotal evidence. I’ve heard math people complain about calling January 1, xx00 the beginning of the decade. BTW, I tried that zero-indexing argument, and was informed that it doesn’t work because there is no year 0. There’s 1 BC, followed by 1 AD. Writing code to handle dates has got to be one of the most thankless jobs ever.
Stolee: I guess it depends who you define as “computer scientists” but both Fortran and MATLAB have their “standard” indexing beginning at 1 and their users seem to view that as normal. (I’m not saying that 1 indexing is better, just that 0 indexing is not 100 percent used with computers.)
I think that one of the possibly notable events in the “mathematical environment” has been the rise of a few number of mathematical content blogs (ie, not just blogs that happen to be written by mathematicians). What will be interesting, and potentially significant, in future years is if these become SOME of the “nucleation points” for determining what’s considered interesting to work on. (In the same way one speech by Hilbert focussed attention on a set of problems for the 20th century.) Of course, blogs may turn out no to be hugely influential: I suspect we’ll only know in retrospect.