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Pierre Deligne Wins Abel Prize For Contributions To Algebraic Geometry
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."
I'm wondering what the use of these prizes is. I thought most of them were created to help the researches, but if you only get it after you've retired, what's the use?
of course the problem is with newer research that it's hard to estimate its longterm value (and if there was no fraud)
but maybe they should just give these guys a nice medal, and invest the rest of the money in current promising research that probably desperately needs it?
I don't know if this was intentional, but I suspect it was: '“The nice thing about mathematics is doing mathematics,” Deligne said. “The prizes come in addition.”' Ha! Math humor is the best humor.
Why can't these guys just graciously accept the prize, without claiming or implying they don't deserve it?
I dunno because their discovery was built on 2500 years of work by their predecessors?
Or am I completely misinterpreting the wording of the stated Weil conjectures?
The maths is entirely beyond me, but I'm gonna go with... yes.
systemd is Roko's Basilisk.
Yes.
http://en.wikipedia.org/wiki/Rational_point
(c.f. http://en.wikipedia.org/wiki/Rational_number)
They are only using integer coordinates. I do not know the math well, but I suspect that is why it is finite. Also, there are different sizes of infinity. For example, the "number set of all numbers" versus the "number set of all positive odd number integers".
From the article: "The Weil conjectures concern the points on algebraic varieties that have integer coordinates (in the case of the circle, x and y must be whole numbers). The number of such solutions — typically, there are only finitely many — can be calculated from a formula called the zeta function."
Some people die at 25 and aren't buried until 75. -Benjamin Franklin
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.
Deligne is a huge mathematician, but :
- Grothendieck give Deligne a lot of unpublished things, to be published;
- Deligne use it, but never publish it,
- Deligne made everything to hide it, and to let others think Grothendieck was fool.
Deligne use (for his only use) the tools given by Grothendieck, but hide and destroyed the spirit of it.
Even without this awful things he does, Deligne is on of the very big mathematician.
But mathematics lose a lot in this malversations.
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.
This is very high level mathematics, well beyond any elementary algebra (what most people think of when they hear "algebra"). This concerns number theory and abstract algebra. One would need several graduate math courses to fully understand the material.
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.
> 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.
Particle physics is a fairly new field -- within the last hundred years, really. We don't *know* that much yet, and so consequently an interested amateur can educate himself on a decent percentage of at least the basics in a few months' worth of free time.
Algebra is a relatively mature field. It's been studied for somewhere around a thousand years (maybe twice that long, depending on what exactly you count). When algebra was understood at the level of detail that particle physics is today, the Cartesian unification (i.e., the relationship between algebra and geometry) hadn't even been imagined yet, let alone group theory or N-dimensional spaces or topology. Heck, after a couple hundred years of study, cutting-edge algebra researchers were still trying to figure out how cubic equations worked. Things have moved a little faster than that for particle physics, because communication between researchers who don't live close to one another is easier now, but it's still going to be a while before particle physics develops as many specialized subfields with as much detail in each of them as algebra has. You need a four-year degree with a major in math just to give you the basic background you need to *start* studying any of the specialties. Even with a four-year undergrad degree, there may still be entire rich subfields of algebra that you haven't *heard of* yet.
Cut that out, or I will ship you to Norilsk in a box.