Math whiz gives lecture at UNL
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By JoANNE YOUNG / Lincoln Journal Star
Sir Michael Atiyah’s father knew his young son had the potential to become a mathematician when he began to notice his son would take the pocket money they used when they traveled to other countries and convert it from one currency into another to make a profit.
Atiyah certainly did become a mathematician, in fact, one of the leading mathematicians and scientists in the world today. He was awarded the Fields medal in 1966 and the Abel prize in 2004, awards at the level of Nobel prizes for mathematicians.
Mathematicians generally are born, not made, Atiyah said.
“I think you’ve got to be born with a certain mathematical talent, otherwise you’re not going to succeed," he said. "Like a musician has to be born with a good musical ear."
After that, a budding mathematician has to be exposed to the right environment in order to flourish, he said, like a plant has to be in good soil to grow.
Atiyah was in Lincoln Friday, brought to the University of Nebraska-Lincoln by the American Math Society, for a public lecture at Kimball Recital Hall. The lecture commemorated the 100th anniversary of Einstein’s“miraculous year,” in which he wrote five of his most important papers.
David Fowler, known as Dr. Fowler to readers of Dr. Fowler’s Math Quiz in the Journal Star’s Homeroom section, speaks the same language as Atiyah and interviewed him for the newspaper. Fowler is an associate professor of teacher education in mathematics at UNL.
The following is an edited transcript of that interview, conducted Friday morning in the UNL math department.
Fowler: People have the perception that Einstein was an isolated clerk who came up with a great idea and announced it to the world. But he was really a very good physicist, too.
Atiyah: There’s a bit of a misconception with Einstein. It’s true he had a job within the patent office. It is true he had trouble getting a regular university job at the beginning. But that’s not too surprising. In those days there weren’t that many. But he had a good education, being taught by the best physicists around. So he was in no way isolated. It is true he worked on his own. He had these great ideas as a young man and he simultaneously produced all these papers in a very short period of time that transformed him from a promising student at the time to suddenly a world-class figure. It was a big jump in the way he was perceived by the outside world.
He wasn’t totally unknown. He had a good background. Although he was in touch with people, he wasn’t working in a group of people. So in that sense he was rather unusual to produce these papers, very very deep papers in a very short time.
But all stories about famous people tend to get exaggerated and caricatured. Biographies of Einstein quite often say when he was in school he was at the bottom of the class. When you look into it, it was a misconception. He was a good student. They say he appeared from nowhere. That can’t happen. Things can’t appear from nowhere. He must have learned things and worked his way up.
Fowler: How do you know when someone is doing mathematics and when they’re doing physics?
Atiyah: It’s a difficult question because first of all it depends on the context of the time. If you had asked (Sir Isaac) Newton, whether he was doing mathematics or physics, I doubt if he’d been able to separate the two out. One was definitely linked to the other.
In recent times they’ve become a bit more separated because it’s easy to become more specialized and some are purely mathematicians and some totally physicists. All physicists have to use a lot of mathematics. In that sense, you can’t be a physicist without a great deal of mathematical sophistication.
If a paper has the word theorem in it, you’re a mathematician. Physicists don’t use the word theorem. They may essentially have the outline of a proof, but they will just say, “We will give convincing arguments in favor of this.” And very often their arguments are partially convincing.
The structure of theorem proof, that’s very much mathematics.
You can’t be a physicist unless you have a really good understanding of the scale on which different things operate. That’s going to be built in, you have a feeling for it. You have an insight into what things mean in practical terms.
Is Newton a physicist or a mathematician? In his case, he created the mathematics in order to solve the problems of physics or dynamics.
Einstein was not a mathematician. He did not create mathematics, he used mathematics. He wasn’t even very good at mathematics. He got help. With his general theory of relativity, he had to go to a mathematician to explain it to him.
(Henri) Poincare, for example, he was a mathematician. He wasn’t quite a physicist. That’s why Einstein beat him to the relativity theory in the eyes of most people. But he was very close.
Fowler: At the international level you work at, do mathematicians have a more universal view of their role rather than having to just keep their country ahead in this race?
Atiyah: Governments everywhere are now saying they put money into education, and research, in order to improve the economy. But the scientific community, on the whole, prefers to adopt the more global humanitarian idea that our work is meant for the benefit of mankind.
We don’t contribute in order to beat the Chinese or the Germans. This kind of competitive approach, which is part of the real life of what governments work on and what determines the funding, is there. But I think they also have to adopt the attitude that science is for the benefit (of) the whole world community.
There is a difference between the attitudes of scientists and of governments, but because they have to work together, it’s a tricky issue. The attitude of being in there for the benefit of mankind is something that can appeal to younger people.
The more fundamental areas of mathematics are farther removed from the front lines, but still the questions are there. Mathematics underpins lots of other things (environmental and medical questions, for example) which, in their turn, have an impact. Environmental questions have to be studied using sophisticated mathematical models (the path of a hurricane, the spread of diseases).
If you want to look at the whole integration of all problems around the world, mathematics is the thing that holds it all together. You need mathematics to address large numbers of global issues.
That can be used to encourage people to take a positive attitude to mathematics and should be done. It’s honest. It’s not a gimmick. You can’t compete against other people. You have to cooperate. Mathematics is a unifying factor that is quite important.
Fowler: How does a mathematical theorem acquire a name?
Atiyah: In mathematics, there is no international body that gives its stamp (such as with naming a comet). Quite often, if you go back through history, you’ll find names incorrectly ascribed. Most of the theorems are actually ascribed to the wrong person. They were around for a long time, and then somebody else wrote a lot of papers about them.
They’re convenient because if a theorem is significant enough, you want a name. Calling something ‘Theorem I’ is all right in a paper, but it doesn’t help much outside. And you can’t always label a theorem by its content.
Nowadays, they usually reflect the people who are mainly concerned in them.
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