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Poincaré Conjecture May Be Solved
Flamerule writes "The New York Times is now reporting that Dr. Grigori (Grisha) Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, appears to have solved the famous Poincaré Conjecture, one of the Clay Institute's million-dollar Millennium Prize problems. I first noticed a short blurb about this at the MathWorld homepage last week, but Google searches have revealed almost nothing but the date and times of some of his lectures this month, including a packed session at MIT (photos), in which he reportedly presented material that proves the Conjecture. More specifically, the relevant material comes from a paper ("The entropy formula for the Ricci flow and its geometric applications") from last November, and a follow-up that was just released last month."
This picture.
;)
Well, made me laugh anyway...
"Hey genius. I assume you mean cubes and, perhaps, pyramids since we're talking 3 dimensions here. Read his definition of "shape" here. Cube and pyramid are the same "shape" as a sphere."
Only someone as fucked up as a mathematician could possibly consider a cube or tetrahedron the same as a sphere. Math and non-sensical concepts, it seems, go hand in hand. Same mentality drove the IEEE to decide that "10" is not "10," but rather is "9.9999999999999999999."
The beauty of mathematics is that it doesn't work like natural sciences. Once something is proved, it is forever proven and correct in maths.
Testing if a proof is correct is not exactly easy. That is, you have to prove the proof is correct, and then prove that proof of the proof is correct. You can have bugs, much like Dunwoody's proof did. In fact, most proofs of this caliber have bugs in them for a couple years until they are found and fixed or the proof falls apart.
I do not know examples of any long times (decades or longer) that a proof has gone before discovering a problem, but it is the fear of many a doctoral candidate in mathematics and theoretical computer science that someone on the committee will bring up some case that shows your theorem is wrong. I saw this happen during a paper presentation once (not a defense), making the entire work wrong in a single stroke. Not pleasant for the presentor, I'm sure.