Peter Lax wins Abel Prize

otisaardvark writes "The prestigious Abel Prize, awarded annually for lifetime contributions to mathematics, has been awarded to Peter Lax [pdf]. Professor Lax, born in Hungary and currently at New York University, has made profound contributions to the theory of partial differential equations, most famously his reformulation of a large class of important PDES (so-called "integrable systems") in terms of Lax pairs of coupled, simplified equations. Read a summary of his achievements here [pdf]."

Comments

Re:Wait what?

[0x461FAB0BD7D2]

If math was directed by practical applications, we would not have many of the items we take for granted today. Cryptography, computers, space exploration are all results of research in mathematics.

I've heard many people wonder what use there is for math beyond its daily uses. However, if people always thought this way, we would not have advanced as a civilization. Someone may yet find a practical use for these "obscure" concepts. Many engineering and science students already know how useful partial differentiation is.

Re:Wait what?

[kisak]

Actually, if you read the different articles, you would have seen that Lax has been working with problems important in physics. I don't know if physics is practial enough for you, but it is hard to deny the influence on modern technology from break-throughs in physics in the last century.

Here is Lax's advive to young mathematicians: "I heartily recommend that all young mathematicians try their skill in some branch of applied mathematics. It is a gold mine of deep problems whose solutions await conceptual as well as technical breakthroughs. It displays an enormous variety, to suit every style; it gives mathematicians a chance to be part of the larger scientific and technological enterprise. Good hunting!"

Re:who cares?

[JaxWeb]

Even if you believe that, and I don't think you do, the stuff this guy did was very relevant to the real world: He worked on Shock Waves (that is, pressure waves), and partial differential equations, among other things (Including computing stuff. Some of the other stuff he has done is a bit abstract, though).

Partial Differential Equations are used in Physics for basically everything (as you mentioned). They are completely relevant to everything. Differential Equations are basically things which describe rates of change. The "partial " bit just says there are other variables involved, pretty much.

Some mathematics seems irrelevant, but it is actually very relevant to the real world. For example, Tensors.

Mathematics is by far the hardest subject humans have ever looked at, and as such, very few understand much of it. Lay persons not understanding does not make mathematics irrelevant. Few people understand how computers work, but computers certainly are not irrelevant.

The Abel Prize

[kisak]

The Abel Prize is named after the brilliant Norwegian mathematician Niels Henrik Abel who died at the age of 26, after living his short life with little money and little support. It is quite amazing that at such young age Abel was able to produce results that put a lasting mark on modern mathematics. Another of the "young dead" in the history of mathematics is Galois, who died at the age of 21 and is remembered for results that expanded on earlier work of Abel. Because of these two and also many other mathematicians who did their best work at very young age, math has got the reputation of being the young man's science.

The Abel prize was introduced as a sort of "Nobel Prize of math" where people are rewarded for results and achievements that have shown themselves to be of lasting value in the field. Alfred Nobel did not want a Nobel Prize in math since he himself saw little scientific value of math! The most prestigious prize in math before the Abel came into being is the Fields medal, but this prize is only given to younger mathematicians (belove the age of 40) that has made break-through results and show promise for the future. The Fields medal is handed out every 4 years while the Abel is handed out every year (first prize was handed out in 2003).

It would have been ironic for Abel if he were to know that such a huge money prize is to be given out in his name, when his whole life he had to live in poverty and fight to get time and money to do his scientific work. The irony of Abel's life is also that Abel himself finally got a professorship in Berlin; but too late, the letter was sent to him two days after his death.

Re:The Abel Prize

[Anonymous Coward]

Wrong. Nobel never married. He was a practical man and all his prizes are awarded for the greatest benefit to mankind (which might be questionable for mathematics). This is why an experiment discovering deuterium or the neutron will receive a prize almost immediately while something more abstract may never receive the prize. Einstein didn't receive the prize specifically for the general theory of relativity, arguably the greatest scientific theory of our time. He won it for the photoelectric effect and his theoretical services to physics (which encompasses many things for a man like Einstein). On a similar note, Hawking hasn't (and probably will never) received the Nobel Prize in Physics.

It should also be noted that even if Nobel was inclined to give a math prize ignoring his perceived impractability of it, there was a large competing prize given away yearly by the King of Sweden. If Alfred Nobel realized how significant his prize would become (becoming the de facto greatest prize of many science fields), he might have taken away the specific praticality aspects and added a math prize (and perhaps other prizes as well--I'd like a Nobel Prize in Geology!).

Re:Wait what?

[mangu]

obscure concepts few people have practical application for

Lax's work may seem obscure, but it has practical applications that are very relevant for many people. Example: simulations in 3d computer games. Look here for more details.

Wiles?

[Alomex]

Question is, how much longer are they going to hold the award from Andrew Wiles of Fermat fame?

Re:Wiles?

[kisak]

I think the Abel Committee is obliged to also honour applied mathematicians, which is one reason Lax was chosen this year. The previous winners, Atiyah and Singer and Serre were all pure mathematicians (like Wiles is).

Andrew Wiles will probably get the prize, but since the prize is very new, there are many important mathematicians to chose from. And even though Wiles is maybe the best known living mathematician to the general public (because of his solution of Fermat's theorem), among mathematicians Wiles is not consider the most dominant mathematician alive today (Serre, for instant, was generally seen as the natural choice for the first prize). Some of the possible worthy winners are also old and will maybe for this reason get the prize before Wiles which is still young and healthy.

Re:who cares?

[MC68000]

Probably a troll, but I'll bite.

There is actually very little mathematics that is not applied. Group theory is very useful for quantum mechanics, and the Lebesgue measure is useful for crystallography. You admit that PDEs may be somewhat of an exception, but even that somehwat is wrong. Most complex models in engineering, physics, economics, and even sociology involve PDEs. But that's not all. Finding exact (which rarely exist) and numerical solutions to PDEs requires not only applied math, but concepts like Sobolev spaces, operator theory, and so much more. Lax's achievement in PDEs is the concept of Lax pairs, which are extremely abstract and require function theory to understand.

In short, all mathematics is useful. Applied math is useful because it gives us insights into the material world, and abstract math gives us insights into both applied math and sometimes even the material world.

No

[bluGill]

Math is one of the few classes where you can learn something truly beautiful that is also useful. Few classes are more useful in day to day life. (reading, perhaps grammar)

Find a good math instructor. In grade school and somewhat in high school, teachers are people who hate math, and so they are unwilling to show you just how much fun it really is.

Re:Mathematics is not a science (neither is medici

[boeman]

Your post is patently ridiculous. First of all, every succesful scientific theory ever has had a foundation built from mathematics (in the hard sciences anyway -- biology and the like are excluded from this claim). Without the work of mathematicians, physics would be nigh impossible.

You also make the claim that medicine is not a science because "understanding the way a healing method works is irrelevant." This statement is not only untrue (if you want to achieve better healing methods than herbal remedies), but also it implies that physicists understand why the universe is the way it is, which they do not. Physicists are quite good at explaining how natural phenomena occur, but there really isn't a good explanation for say, why gravity exists or why inertial mass and gravitational mass are (or appear to be) the same. Physics is simply a model of reality based upon observation, logic, and induction, and any one of which may or may not be correct in the first place.

Finally, (and I do take this a little personally) you make a similar claim for engineering as you do medicine. Do you mean to imply that, say, aerospace engineering (rocket science, if you will) is not science? If you are trying to tell me that the men who put Neil Armstrong on the Moon did not understand why their spacecraft worked, you are either mentally handicapped or an elitist snob. The same can be said of the other engineering disciplines as well--you just seem to lack experience with them.

Sorry to say, but he is right.

[LuckyStarr]

[ ] You understand what the "scientific method" is.
[X] You are easily offended.