There was a time when a lot of jazz musicians I got acquainted with in college died, and another time when a lot of movie directors I found out about died. Now it seems that a few mathematicians whose work I had studied had died.
First off is the father of chaos theory, Edward Lorenz. I attended a course on chaos theory and I came to realize that it is not simply a scientific fad that has made its way into popular culture, but it is a very important way to study systems. One of the important implications of chaos theory is that it is very futile to predict the behaviour of sufficiently complicated systems.
Unfortunately some of the people that I work with don’t really understand this, in spite of the fact that one of them holds an advanced degree from Lorenz’s university. They have an exaggerated belief in their ability to predict events that take place in the future, or their ability to make sense out of it, rather than to do the more sensible thing and just plan for contingencies. They’re also too smart to listen to what I have to say.
I may have blogged about chaos theory at length before. There’s too much to explain over here. People who are interested can just go read this nice book that my professor recommended, “Chaos” by James Gleick
Another person who died was Kiyoshi Ito. I had heard that it was possible, 10 years ago, to earn shit loads of money as a maths geek by studying a maths technique called stochastic differential equations. In the 1970s, a few people – Myron Scholes and Fisher Black came up with a way to use sexy fancy mathematics to make rapid investment decisions on complex financial instruments called derivatives. One of their discoveries was the Black Scholes option pricing model, which calculates the probable value of stock options. To do this they had to build upon a lot of important and cheem work that Ito laid down for stochastic differential equations.
Scholes and Merton, another one of their maths buddies, joined a hedge fund, Long Term Capital Management. Both of them were awarded the Economics Nobel Prize for their “contribution” in 1997. In 1998, LTCM blew up and went bust. Oops.
What went wrong? Apparently one of the central assumptions – that you can use a lot of teeny weeny normal distributions to model the movement of stock markets. But that assumption does not square very well with reality. Benoit Mandelbrot, who is a very important figure in chaos theory (and who also likes to tell a lot of old farts in academia that their ideas are wrong) developed some ideas about a better and more accurate way to assess risk. Unfortunately the maths in his system is much more difficult to work with and he does not have something with the theoretical elegance of the Black Scholes model.
In the meantime, a lot of fingers have been pointed at hedge funds for their role in exacerbating the current financial crisis. This will be debated for a long time yet. This is not to point fingers at Ito, since he only did the maths part and said nothing about applications for finance. Ito’s work has a lot of other applications which make more sense, in electrical engineering, for instance.
The last person is Henri Cartan. I am not that familiar with Henri Cartan’s work. But there was once I wanted to learn about complex analysis, and I ended up picking up a book about it. It is probably the same textbook as the one mentioned in his obituary. Cartan was a member of the Bourbaki group that helped develop the concept of a proof to be something that is completely rigorous, and not leave anything to the imagination. A bit like asking a sexy woman in front of you to please remove the bikini because after all you are almost naked anyway. On one hand this was intensely irritating because my professors would be nitpicking every part of every maths proof I ever did as homework. But it was great for the development of maths because when you are so rigorous with everything, all the ideas behind the proof are shown clearly, and then you can sometimes derive some more connections between ideas, and at the same time drive more maths research.
First off is the father of chaos theory, Edward Lorenz. I attended a course on chaos theory and I came to realize that it is not simply a scientific fad that has made its way into popular culture, but it is a very important way to study systems. One of the important implications of chaos theory is that it is very futile to predict the behaviour of sufficiently complicated systems.
Unfortunately some of the people that I work with don’t really understand this, in spite of the fact that one of them holds an advanced degree from Lorenz’s university. They have an exaggerated belief in their ability to predict events that take place in the future, or their ability to make sense out of it, rather than to do the more sensible thing and just plan for contingencies. They’re also too smart to listen to what I have to say.
I may have blogged about chaos theory at length before. There’s too much to explain over here. People who are interested can just go read this nice book that my professor recommended, “Chaos” by James Gleick
Another person who died was Kiyoshi Ito. I had heard that it was possible, 10 years ago, to earn shit loads of money as a maths geek by studying a maths technique called stochastic differential equations. In the 1970s, a few people – Myron Scholes and Fisher Black came up with a way to use sexy fancy mathematics to make rapid investment decisions on complex financial instruments called derivatives. One of their discoveries was the Black Scholes option pricing model, which calculates the probable value of stock options. To do this they had to build upon a lot of important and cheem work that Ito laid down for stochastic differential equations.
Scholes and Merton, another one of their maths buddies, joined a hedge fund, Long Term Capital Management. Both of them were awarded the Economics Nobel Prize for their “contribution” in 1997. In 1998, LTCM blew up and went bust. Oops.
What went wrong? Apparently one of the central assumptions – that you can use a lot of teeny weeny normal distributions to model the movement of stock markets. But that assumption does not square very well with reality. Benoit Mandelbrot, who is a very important figure in chaos theory (and who also likes to tell a lot of old farts in academia that their ideas are wrong) developed some ideas about a better and more accurate way to assess risk. Unfortunately the maths in his system is much more difficult to work with and he does not have something with the theoretical elegance of the Black Scholes model.
In the meantime, a lot of fingers have been pointed at hedge funds for their role in exacerbating the current financial crisis. This will be debated for a long time yet. This is not to point fingers at Ito, since he only did the maths part and said nothing about applications for finance. Ito’s work has a lot of other applications which make more sense, in electrical engineering, for instance.
The last person is Henri Cartan. I am not that familiar with Henri Cartan’s work. But there was once I wanted to learn about complex analysis, and I ended up picking up a book about it. It is probably the same textbook as the one mentioned in his obituary. Cartan was a member of the Bourbaki group that helped develop the concept of a proof to be something that is completely rigorous, and not leave anything to the imagination. A bit like asking a sexy woman in front of you to please remove the bikini because after all you are almost naked anyway. On one hand this was intensely irritating because my professors would be nitpicking every part of every maths proof I ever did as homework. But it was great for the development of maths because when you are so rigorous with everything, all the ideas behind the proof are shown clearly, and then you can sometimes derive some more connections between ideas, and at the same time drive more maths research.
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