Monday, October 13, 2008

The Mark of The Kiyoshi Ito



"Kiyoshi Itô is the first winner of the Gauss Prize for applications of mathematics. The new prize is named for Carl Friedrich Gauss, one of the greatest mathematicians of all time, whose work demonstrated the ability to apply mathematics to many sorts of problems in physics, astronomy and engineering. The prize is awarded jointly by the Deutsche Mathematiker-Vereinigung (DMV = German Mathematical Union) and the International Mathematical Union (IMU), and administered by the DMV. It consists of a medal and a monetary award (currently valued at 10,000 Euros).
Kiyoshi Itô, aged 90, received the prize for his work on stochastic analysis, allowing the study of stochastic processes by means of what are now known as "stochastic differential equations." These have found applications all over science, and also, perhaps most famously, in mathematical finance via the Black-Scholes equations. Though Itô first developed these ideas in the 1940s, it took quite a while for mathematicians to understand and appreciate his results. Only after 1954, when Itô visited the Institute of Advanced Studies, did his ideas begin to have their true impact. Today, stochastic analysis is a basic tool in the study of stochastic processes and plays a crucial role in many branches of applied mathematics. "An Early Nice Use of Ito's Integral

12 comments:

Mr roT said...

Looks like fun. Bessels from BS (probs). Sorry. Couldn't resist.

My Frontier Thesis said...

This idea of revisiting previous ideas to see if anything has been overlooked (and that it's important for all disciplines) is an argument I had a couple weeks ago. I merely mentioned that a girl who had a "Darwin" sticker on her car asked me how good the naturalist's thoughts were when I told her I was delightfully working my way through "The Descent of Man." I said, "You haven't read Darwin?" She said, "No: there's no need to!" Perhaps, perhaps. I related this story to another, and she, as the saying goes, flew off the handle, telling me that someone can believe in Evolution without having read Darwin. I said, "Yes, but that's not the point: there are many leaps and jumps the naturalist makes. However, the broader point is that it's important to revisit otherwise unvisited sources from the past, as they may prove to offer a new direction to take scholarship..."

Your thoughts, gentlemen?

Arelcao Akleos said...

I agree, of course, MFT. But then I share your affinity for taking the depth of history as essential for most true understanding, as much in science as in other fields....
However, it's unlikely the other three FCPers share this view quite so fulsomely. So, AI, JJ, Le Pew. What sayeth yee?

Mr roT said...

AA, I don't understand the qn. I thought this thread was about using Wiener measure to re-solve a whose solutioin was 'deterministically' solved a century before.

Math is not about revisiting old theorems to see if they are still true. This paper (and it is definitely worthy in my estimation) is about getting to know new math (Ito-Wiener-Feynman) by working out an old problem that everyone understands with a new powerful tool that has more general application than the old method.

For example This and more importantly (to my mind) this. Feff uses a lot of Martingales in his real paper.

So, I think I am saying phooey on you. Revisiting goddamned Bessel is not interesting for Bessel. It's a primer on how to calculate in a new technique.

In math, old junk is old junk.

Pepe le Pew said...

Thanks for the explanation aa.
I wish I'd known of this a while back...

Mr roT said...

Pepe, why do you wish you knew about this a while back? You think you can get more chicks in Probs than in Geop? Not fucking likely. Barbie says "math is hard," but she likes oilmen if the PetE groupies I remember from undergrad days were any indication.

Arelcao Akleos said...

"Math is not about revisiting old theorems to see if they are still true. This paper (and it is definitely worthy in my estimation) is about getting to know new math (Ito-Wiener-Feynman) by working out an old problem that everyone understands with a new.."

JJ, so you think you are arguing contra someone who is opposed to what you wrote??. MFT brought in the notion of "revisiting previous ideas to see if anything has been overlooked". I agreed with him that such a notion was worthwhile. And then stated that it is unlikely that the three other FCPers "share this view quite so fulsomely".
Which, as you quickly made apparent, was corroborated in your instance.
Now you raise a different notion; to wit that revisiting an older idea such that "This paper (and it is definitely worthy in my estimation) is about getting to know new math (Ito-Wiener-Feynman) by working out an old problem that everyone understands with a new powerful tool that has more general application than the old method."
Well, I agree with you there.

Neither MFT, nor you, nor I, ever said anything close to:
"Math is about revisiting old theorems to see if they are still true".
So.... where'd you get that notion?

C'mon, JJ, drink up that heady Ginger Ale.

Mr roT said...

AA, you're an idiot if you didn't understand what I meant and doubly so if you expected me to understand your question. I suggest you take your bottle of sarsaparilla and shove it rectally till you see the twin bright lights of reason and grammar.
Meanwhile, I will mentally revisit the Gingerman (blissfully free of Obamananians diggin' that positive vibe as at JHBH) and try my best to determine if it is still true that it is a great venue in which to insult women's studies twits with Dartmouth bandanas.

Mr roT said...

Remember what CB said, AA. Coffee too late implies gay. Sorry. It's a theorem.

Arelcao Akleos said...

You misheard your fellow Ginger types. They were talking about their serums.

Mr roT said...

What serums? Serums of Truth (good old capital T Truth like we have here in redneckland) is what is to be drunk at the $G$-man. I would have gotten thrown in sensitivity camp for saying what I did last Sat night in Houston in Cambridge instead!

My Frontier Thesis said...

JJ, I hope I'm not butchering anything here, but I think your statement below reads a bit contradictory (the former and latter statements). Essentially, in the latter component, that's what AA and I said in a post or two above the phrase of yours. For ease, I put in italics here, as I think we're all into at least our 7th beer of the evening.

JJ said:

Math is not about revisiting old theorems to see if they are still true. This paper (and it is definitely worthy in my estimation) is about getting to know new math (Ito-Wiener-Feynman) by working out an old problem that everyone understands with a new powerful tool that has more general application than the old method.

Yes, working out an old problem with a new powerful tool. Revisiting the past with new tools of the present. A while ago Hubble telescope technology was used to read burned up papyrus papers that, if memory serves, contained previously missing information from Archimedes. And, JJ, if I'm not mistaken, isn't that what you would call, "Judging the past from our present day perspective?"

Swing away, Texas. The high Plains is above you (couldn't resist; I'll be able to respond tomorrow evening, if this post isn't buried in shit by then).