Pierre Deligne Wins Abel Prize For Contributions To Algebraic Geometry 55
ananyo writes "Belgian mathematician Pierre Deligne completed the work for which he became celebrated nearly four decades ago, but that fertile contribution to number theory has now earned him the Abel Prize, one of the most prestigious awards in mathematics. The prize is worth 6 million Norwegian krone (about US$1 million). In short, Deligne proved one of the four Weil conjectures (he proved the hardest; his mentor, Alexander Grothendieck, had proved the second conjecture in 1965) and went on to tools such as l-adic cohomology to extend algebraic geometry and to relate it to other areas of maths. 'To some extent, I feel that this money belongs to mathematics, not to me,' Deligne said, via webcast."
Re:let's start a giant math debate (Score:2, Informative)
Yes.
http://en.wikipedia.org/wiki/Rational_point [wikipedia.org]
(c.f. http://en.wikipedia.org/wiki/Rational_number [wikipedia.org])
Re:let's start a giant math debate (Score:5, Informative)
No.
From your comments on the matter I suspect it would be challenging to even begin to explain this to you, since it looks like you are interpreting "field" as "area". You're about 3 semesters of algebra away from understanding the vocabulary, let alone the purpose and function of these conjectures.
Note: this isn't meant as a slam, and you shouldn't feel bad (honestly!). Cutting edge pure math research is so far out there it's really difficult to jump in as an enthusiast in the way that interested parties can casually follow things like particle physics. When I was reading algebraic topology as a phd student (I flunked out... wasn't good enough, so feel free to take this with a grain of salt) I couldn't even begin to explain what it was that I was doing to people, even very smart people, just because of how abstract it all is.
Re:Any matematician there? (Score:4, Informative)
The short (and flip) answer is: who cares? Certainly not the researcher, and neither do I.
But that's not very helpful, or easy for somone who isn't a pure mathematician to understand. However, it is frequently the reality of the situation. Pure math does not concern itself with application or any dirty real world situations (hence: pure). Algebraic geometry as a field of study was popular in the pure math boom at the beginning of the 20th century and then fell out of favor in the middle part as it was considered to be a dead field (this happens from time to time when practical avenues are all exausted, limits are reached on computational methods, and departments dismantle research groups either intenionally or naturally as interests are turned elsewhere). The late 20th c. saw a resurgence precicely because of high level computer science turning back some of the issues listed parenthetically above. Parts of the weil conjectures have connections to lie algebras, which are very popular right now due to applications to physics and computer science.
Re:Any matematician there? (Score:2, Informative)
What? There is no doubt there is an interest, and even a large interest in computational algebraic geometry. But this wasn't responsible for the resurgence of algebraic geometry.
Weil formulated his conjecture by pretending that he had this mathematical tool known as (a good) "cohomology" (theory). He didn't have such a tool, but if he did, the Weil conjectures are exactly what this tool would allow him to prove.
The late 1930's saw the fall of the Italian school and Zariski et al started working on reformulating the foundations. Using the tools of homological algebra developed in the 40's and 50's along with the reformulation by Zariski and others, algebraic geometry saw a rebirth with Grothendieck who (a) layed the foundations of modern algebraic geometry in his monumental work EGA and (b) used the abstractness of homological algebra to formulate versions of "cohomology" which are suitable for the spaces one encounters in algebraic geometry. It was Deligne who was finally able to use this to prove the last of the Weil conjectures.
It had nothing to do with computers.