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Pierre Deligne Wins Abel Prize For Contributions To Algebraic Geometry

Unknown Lamer posted about a year and a half ago | from the making-you-feel-dumb dept.

Math 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."

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Rest of his quote. (0)

Anonymous Coward | about a year and a half ago | (#43224317)

But in a fuller extent, I'm going to be happy to spend it...

Re:Rest of his quote. (0)

Anonymous Coward | about a year and a half ago | (#43224349)

Unlike Perelman though.

I might be the first to point out... (0)

Anonymous Coward | about a year and a half ago | (#43224385)

The first Deligne number has just been assigned. Pierre Deligne's number is 0.

Belgium? (0)

Anonymous Coward | about a year and a half ago | (#43224453)

"Belgium" is the most offensive word in the galaxy. This is a declaration of war!

Where's my towel?!

Quoted... (0)

Anonymous Coward | about a year and a half ago | (#43224457)

'To some extent, I feel that this money belongs to mathematics, not to me,' Deligne said, via webcast, to which Deligne quickly followed up with "...but the money's mine bitches!!"

Why so much later?? (3, Insightful)

Racemaniac (1099281) | about a year and a half ago | (#43224467)

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?

Re:Why so much later?? (0)

Anonymous Coward | about a year and a half ago | (#43224549)

So that people who will pursue them, and be good slaves^W^W^Wstrive for excellency.

Re:Why so much later?? (3, Funny)

Xest (935314) | about a year and a half ago | (#43224575)

To encourage others. Even if it can't now be used for research there will at least be some people saying "Oh, so being a mathematician is a path to becoming a millionaire".

That will encourage some kids and uni/college students. It's an attempt to try and do something about the divide in society between the recognition given to sports stars, celebrities, manufactured pop stars, and other overly glamorised non-contributors to the human race who generally get lavished in riches for nothing other than being a fucking idiot publicly and the people who do actually contribute like scientists.

There's still a long way to go because you'll still get paid way more for nothing other than the ability to kick a ball around a field effectively than you will for curing cancer, inventing the world wide web, or sending people to the moon and robots to Mars, but at least it's an attempt at doing something about the problem of western society where idiocy is valued far more greatly than intelligence and competence.

Mod this properly! (1)

nicodoggie (1228876) | about a year and a half ago | (#43231075)

Why is this not modded insightful??

Re:Why so much later?? (0)

Anonymous Coward | about a year and a half ago | (#43227937)

Publicity. Giving away $1 million makes a bigger buzz than just a medal.

Re:Why so much later?? (0)

Anonymous Coward | about a year and a half ago | (#43228245)

The Abel prize was only created in 2001.

" 'To some extent... (1, Redundant)

QilessQi (2044624) | about a year and a half ago | (#43224527)

... I feel that this money belongs to mathematics, not to me,' Deligne said, via webcast."

He then went on to demonstrate mathematically that "some" is less than "all" by grabbing the check and running for the hills.

I suspect this comment was on purpose (4, Funny)

blankinthefill (665181) | about a year and a half ago | (#43224537)

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.

Re: I suspect this comment was on purpose (1, Funny)

wonkey_monkey (2592601) | about a year and a half ago | (#43224745)

Math humor is the best humor.

I don't know about that. I often find it has the power to divide a room.

Re: I suspect this comment was on purpose (1)

kamapuaa (555446) | about a year and a half ago | (#43224761)

OCT31=DEC25! Wocka Wocka!

Re: I suspect this comment was on purpose (1)

Dishwasha (125561) | about a year and a half ago | (#43226409)

Am I supposed to read that as "OCT31 equals DEC25.....NOT :P" or "OCT31 equals DEC25, surprise!"?

Re: I suspect this comment was on purpose (0)

Anonymous Coward | about a year and a half ago | (#43226615)

Surprise!

Re: I suspect this comment was on purpose (1)

blankinthefill (665181) | about a year and a half ago | (#43224789)

I don't know about that. I often find it has the power to divide a room.

True, but you can't deny that minus the math haters, it provides several times the hilarity of boring, non-math humor!

Re: I suspect this comment was on purpose (1)

Sulphur (1548251) | about a year and a half ago | (#43225209)

Math humor is the best humor.

I don't know about that. I often find it has the power to divide a room.

And this medal has the power to ward off the plague of bad arithmetic.

Re: I suspect this comment was on purpose (1)

jonadab (583620) | about a year and a half ago | (#43234917)

On the other hand, math can also function to transform a group, or even form a union between groups.

Re: I suspect this comment was on purpose (1)

jonadab (583620) | about a year and a half ago | (#43234961)

And, of course, manifold humor is part of the field.

Re: I suspect this comment was on purpose (2)

K. S. Kyosuke (729550) | about a year and a half ago | (#43225819)

Math humor is the best humor.

What, humor has a total order defined on it?

Re: I suspect this comment was on purpose (1)

Anonymous Coward | about a year and a half ago | (#43226317)

Partially.

Re: I suspect this comment was on purpose (0)

Anonymous Coward | about a year and a half ago | (#43227759)

Don't go off on a tangent about math humor, please.

Again...??? (-1)

Anonymous Coward | about a year and a half ago | (#43224645)

Why can't these guys just graciously accept the prize, without claiming or implying they don't deserve it?

Re:Again...??? (2)

divisionbyzero (300681) | about a year and a half ago | (#43224689)

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?

Re:Again...??? (1)

Sulphur (1548251) | about a year and a half ago | (#43225315)

Why can't these guys just graciously accept the prize, without claiming or implying they don't deserve it?

What he said was !=0, or twern't nothing.

let's start a giant math debate (1)

slashmydots (2189826) | about a year and a half ago | (#43224661)

So I'm a software programmer and used to be a math tutor. My college hired me after I finished 18 week self-paced Algebra in 7 weeks. That's about all the further I get into besides Quickbooks and customer PC build quotes but this still doesn't seem right to me. Am I understanding this correctly?
Weil wanted to prove that just because an area has a finite length, that means there's an actual, real number of individual points in it? Um, if you think there's 1 million points in an area or line or whatever, make the points smaller and you've got 2 million for example. Think that's the answer, make the points smaller again. This is similar to black hole singularity theory. What is the width of a black hole singularity? Wide enough to exist but infinitely small besides that...in other words, not a value that can be expressed as a real number. The same goes for points in a geometrical area, so there are infinite points. How could anyone prove something that's not true at all? Or am I completely misinterpreting the wording of the stated Weil conjectures?

Re:let's start a giant math debate (2)

wonkey_monkey (2592601) | about a year and a half ago | (#43224737)

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.

Integers (2)

schneidafunk (795759) | about a year and a half ago | (#43224801)

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."

Re:let's start a giant math debate (4, Informative)

spopepro (1302967) | about a year and a half ago | (#43224805)

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:let's start a giant math debate (1)

schneidafunk (795759) | about a year and a half ago | (#43224869)

I think you just described my level of math knowledge as well. I was trying to understand this explanation of Weil conjectures [ucdavis.edu] and couldn't make it past the first paragraph without being lost.

Re:let's start a giant math debate (1)

Anonymous Coward | about a year and a half ago | (#43225835)

I think you just described my level of math knowledge as well. I was trying to understand this explanation of Weil conjectures [ucdavis.edu] and couldn't make it past the first paragraph without being lost.

You might want to try reading Gowers's account of the work of Deligne. It's a short article, and slightly less technical than the one you "read". Here : Pierre Deligne's Work [wordpress.com]

Re:let's start a giant math debate (2)

jonadab (583620) | about a year and a half ago | (#43235411)

> 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.

Re:let's start a giant math debate (0)

Anonymous Coward | about a year and a half ago | (#43240331)

I don't think the two fields are that far off from each other practically speaking. While you may be able to learn about the names of different particles from a pop-sci book, the actual meat of the field is not taught until graduate school. People might not have as much interest in abstract math, but you still find pop-math descriptions of things like the Banach-Tarski paradox without really covering much of the math behind it. I think the difference you are trying to paint between the two is mostly (but not completely) superficial, and more a result of the slightly less abstract results of particle physics and the larger volume of material/interest that gives it a more approachable veneer.

Re:let's start a giant math debate (0)

Anonymous Coward | about a year and a half ago | (#43253299)

I love that you used the Banach-Tarski paradox as an example! That's some potent evil Lovecraftian math lol XD

Sincerely,
an anonymous "integer dabbler" coward.

Re:let's start a giant math debate (2)

tbid18 (2495686) | about a year and a half ago | (#43225361)

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.

Re:let's start a giant math debate (1)

Anonymous Coward | about a year and a half ago | (#43226939)

Part of the confusion is that the use of "algebra" in advanced math is far broader and involves math far higher than what is covered in "Algebra" and "Algebra II" style classes you see in high school or in undergraduate classes. The difference is almost on par with calling an "Introduction to using MS Office" class "Computer Science 101." The first taste of the more advanced math would be an abstract algebra course taken, typically taken by a first or second year math major, cover topics like group theory, ring theory, and fields. Some of the more advanced fields are not even covered until graduate school, followed by, incredibly narrow specialization at times, research after that.

The Weil conjectures can be traced back to the problem of trying to find solutions of certain categories of algebraic equations where the values of the solution are rational numbers. While it is pretty easy to see there are an uncountable number of infinite points on the curve traced out by a parabola or a circle, the number of points where both x and y coordinates are rational takes a bit more thinking. And when treating curves like those more generally, it gets complicated fast. The Weil conjectures are concerning properties of a function related to a more abstract sense of such problems, which turn out to also be important for showing connections between such properties and other broad areas of mathematics. But beyond saying there is some beauty in the connections such work makes between math over discrete points and math related to continuous sets, it quickly becomes difficult to go into detail without some background, e.g. what a field [wikipedia.org] is, considering this deals with a very specific kind of field.

I feel that this money belongs to mathematics (1)

Ryanrule (1657199) | about a year and a half ago | (#43224673)

If that money belongs to mathematics, then we get to claim all HFT hedge funds as well.

What should he buy? (1)

kramer2718 (598033) | about a year and a half ago | (#43224893)

Give that he spent decades of his life slaving away over complex mathematical proofs, he really ought use his well deserved prize money to buy

Hookers

Re:What should he buy? (1)

Anonymous Coward | about a year and a half ago | (#43225005)

... and then he can tell his wife that he's with his hookers; his hookers that he's with his wife; and go to the office and do more math!

Re:What should he buy? (1)

magic maverick (2615475) | about a year and a half ago | (#43225145)

Assuming by "hookers" you mean "prostitutes", then you don't buy them. Just like you don't sell your body when you go to work, neither do prostitutes. Prostitutes sell a service, just like hair dressers and masseurs do. So, really, you should say that the person should buy, not "hookers", but rather "the services of hookers".

Moreover, you could probably get free sex with a million dollars, even if you are 68.

Re:What should he buy? (0)

Anonymous Coward | about a year and a half ago | (#43225331)

You know, your objection makes sense in a political discussion on the legality of prostitution. There it is usually very important to distinguish a sexual service from slavery.

But throwing that objection into an everyday discussion just makes you seem like a cunt.

Re:What should he buy? (1)

jewens (993139) | about a year and a half ago | (#43231907)

I believe the standard prostitute EULA describes it as "a time-constrained, non-transferable license."

Re:What should he buy? (1)

PolygamousRanchKid (1290638) | about a year and a half ago | (#43225641)

Well, Nobel prize laureate Richard Feynman his lunch breaks in strip bars, scribbling equations on napkins. So there is a precedent there . . .

Any matematician there? (-1)

Anonymous Coward | about a year and a half ago | (#43225039)

I was wondering if somebody could explain me the practical applications of the Weil conjectures.
I guess this can be applied to cryptography but it may be also applicable to computer theory.

Re:Any matematician there? (3, Informative)

spopepro (1302967) | about a year and a half ago | (#43225323)

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? (2, Informative)

Anonymous Coward | about a year and a half ago | (#43227349)

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.

Re:Any matematician there? (1)

jonadab (583620) | about a year and a half ago | (#43235543)

Nobody can explain it to you because nobody really knows yet. It's impossible to know in advance what all the practical applications will be for a new development of this kind. When number theorists first started looking at complex numbers, they could not possibly have predicted that this research would eventually become important for electrical engineering and fluid dynamics.

Deligne is a huge mathematician, but (4, Funny)

Anonymous Coward | about a year and a half ago | (#43225147)

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.

Re:Deligne is a huge mathematician, but (1)

Anonymous Coward | about a year and a half ago | (#43225697)

You can find recolte et semailles by Alexandre Grothendieck on http://acm.math.spbu.ru/RS/

I was shocked to see he wasn't black (1)

Anonymous Coward | about a year and a half ago | (#43227675)

Weren't you?
Since "We're all the same", and 'Diversity is our strength", or so our Jewish 'masters' keep telling us, over and over again.

I bet you would much rather live in an all white country.

After all, it seems as if half the third world would much rather live among white people than THEIR OWN KIND...

Appropriate name (0)

Anonymous Coward | about a year and a half ago | (#43227793)

The guy's name is "deligne", meaning "of line" in french, but also homophone of "deux lignes", "two lines".

Algebraic geometry is appropriately a great field for him.

Mathematics deserves the winnings (0)

Anonymous Coward | about a year and a half ago | (#43228361)

I will cheerfully give him the ABA and account number for "mathematics" for him to wire the funds to.

JJ

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