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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]."
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.
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!"
--- guns don't kill people, people with guns kill people ---
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.
- Jax
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.
E = m c^3 Don't drink and derive E = m c^3
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.
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.
[ ] You understand what the "scientific method" is.
[X] You are easily offended.
Meme of the day: I browse "Disable Sigs: Checked". So should you.