   Mathematics today
  What''s being researched in the field of mathematics today?  
  Hmmm... Fermat''s Last Theorem? Nope, already solved. How about proving the Riemann hypothesis? :D    Firebird Entertainment;  combinatorics  ;  That is like asking how many different grains of sand  there are on a large beach, but here are a few to help you out: Differential Geometry, Algebraic Topology, Lie Algebras, Operator Algebras, Partial Differential Equations, Number Theory,  Topology of Manifolds and Dynamic Systems. All of it is interesting stuff, in response to the other post I doubt we will see a proof of the Reimann Zeta Hypothesis any time soon.--------------------------------------------------------"This just goes to show that there are only two kinds of people in this world, stupid people... and me." [edited by - Vorador on November 20, 2002 9:13:23 PM];  I get a newsletter once a week via email that talks about all the latest work going on in the field of abstract mathematics, computer science and physics. It''s really cool, although I admit that I don''t always get to read all of it. The specific email that I get is addressed to all academic researchers in the Montreal area, but I''m certain that there exist similar newsletters with a more general distribution. Go look it up, and at the very least you''ll find a few interesting sites which will more than answer your question (as Vorador points out, there''s simply no easy answer because your question is too vague).  ;quote:Original post by Graylien   Go look it up, and at the very least you'll find a few interesting sites which will more than answer your question (as Vorador points out, there's simply no easy answer because your question is too vague).  I'm not actually interested in learning math, I'm just curious about what's going on in the field. It doesn't seem like there's much new to learn, just looking deeper into what has already been come up with.[edited by - mtw on November 20, 2002 12:16:30 AM];  Graph Theory still has a lot of unexplored territory.There''s scads of topics that are still under research, mtw. However, they''re not necessarily among the kind of stuff you''d touch on in a standard (non math major) undergraduate education.  ;quote:Original post by mtw   I'm not actually interested in learning math, I'm just curious about what's going on in the field.  I realize this, but I stick by my advice. You know how there's always some news items on the main GameDev page? Well, just as this is a site for game programming, there are sites for advanced mathematics. Just a couple of minutes a week and I think you'll have your question answered (i.e. you'll be able to compile a list 100 times the size of the one Vorador has already provided).Your question is frustrating because it's impossible to answer.quote:Original post by mtw   It doesn't seem like there's much new to learn, just looking deeper into what has already been come up with.   It does seem like that, doesn't it? Fortunately, nothing could be further from the truth. In math (or any other field for that matter), what were seeing now is a very high degree of specialization. Gone are the days when one brilliant mind can rewrite all of human science with one publication (e.g. as Newton and Einstein did). Because people learn only about the major breakthroughs of science in school, they assume that every hundred years or so all scientific knowledge must be tossed aside when some new way of thinking comes along.Most people are able to grasp concepts such as "gravity," "electrons," or even "relativity." However, modern research is so deepand so specializedthat most people lack 99% of the background knowledge to even beginto talk about recent breakthroughs. As a result, many people wrongly think that we are in a period of scientific stagnantion ... and will remain so until the next Gauss, Lagrange, Newton, Euler or Einstein comes along.[edited by - Graylien on November 21, 2002 1:05:09 AM];  Computers are allowing exploration into fields that have only been theorized before.  There''s a lot of interest in random processes lately, spurring research into areas like adaptive filtering.  If you want to know where the money goes, it''s there--creating the perfect stock market model.  ;MathWorld''s list of unsolved problemsquote:The specific email that I get is addressed to all academic researchers in the Montreal area  Graylien, out of curiosity, are you an acadademic researcher in the Montreal area? If so, where?Cédric  