Speech by gelfand, a great Ukrainian-born mathematician, at a 90th birthday party

Israel Gelfand (2 September 1913 – 5 October 2009) was a Jewish mathematician born in Odessa, Ukraine. Galfant showed extraordinary mathematical ability as a teenager, although his family was poor and he could not go to school due to illness, but he taught mathematics by himself, and at the age of 19, without attending high school or university, he was directly admitted as a graduate student of Moscow University, under the tutelage of the famous Russian mathematician Kolmogorov. The latter allowed Gell-Fondt to work in the then emerging field of functional analysis. At the age of 28, he independently solved Hilbert's 7th problem. In addition, he has made important contributions in many fields such as harmonic analysis, group representation theory, integral geometry, and upper cohomology, and has even made achievements in biology and physiology. In 1939 he was elected Corresponding Member of the USSR Academy of Sciences, and in 1978 he was awarded the first Wolf Prize in Mathematics with Siegel. The following is Galfant's speech at his 90th birthday dinner on September 2, 2003.

Written by | Gelfand

Translate | Lin Kailiang

It was a pleasure to meet you all. I was asked many questions. I will try to answer a few of them.

The first question was, "Why am I still able to do math at my age?" ”

Second: "What do we have to do in mathematics?" ”

Third: "What is the future of mathematics?" ”

I think these issues are too specific. Instead, I'll try to answer my own question:

"What is mathematics?" (Laughter.)

Let's start with the last question: What is mathematics?

My point is that mathematics is part of culture, just like music, poetry, and philosophy. I address this in my report on the meeting. There I have already mentioned the closeness of the style of mathematics to the style of classical music and poetry. I am pleased to find the following four common characteristics: first, elegance, second simplicity, third precision, and fourth incredible ideas. The combination of the four things of beauty, simplicity, precision, and incredible thought is at the heart of mathematics, the heart of classical music. Classical music refers not only to the music of Mozart, Bach, and Beethoven, but also to the music of Shostakovich, Schnitke, shoenberg (the last one I know less). All of this is classical music. Moreover, I think the above four characteristics have always been presented in them. For this reason, as I explained in my report, it is no accident that mathematicians love classical music. They like classical music because it has the same style of psychological organization.

There is another aspect of mathematics that is similar to classical music and poetry: they are both languages that understand many things. For example, in my report I discuss a question that I have an answer to but do not want to answer but do not want to answer: Why did the great Greek philosophers study geometry? After all, they are philosophers. They studied geometry as a philosophy. Later, the great geometrists followed them and followed the same tradition of bridging the gap between vision and reasoning. Euclid's work, for example, sums up the achievements of his time in this regard. But that's another topic.

An important aspect of mathematics is that it is a language of need for different fields—physics, engineering, biology. The most important word here is adequate language. We have languages that are right for needs and languages that are not. I can give examples. For example, using quantum mechanics in biology is not the language of need, but the study of gene sequences with mathematics is the language of need. Mathematical language helps organize many things. But this is a serious subject, and I don't want to go into the details.

Why is this topic important now? This is because in our time we have "change". We have computers that can do anything. We are no longer bound by two operations—addition and multiplication. We also have many other tools. I'm sure that within 10 to 15 years, mathematics will be completely different from what it used to be.

The next question is: How can I still do math at my age? The answer is very simple: I am not a great mathematician. I'm serious. I've been just a student all my life. I've been studying hard since the very beginning of my life. For example, now when I listen to conference presentations and read handouts, I find that there is still so much I don't know and that I have to learn. So I've been learning. In this sense, I am a student – and by no means a "chief "chief "Führer".

I would like to mention my teacher. I can't fully list all my teachers because there are so many. When I was young—about fifteen or sixteen—I started learning math. I didn't get a formal education, never enrolled in a university, and I "skipped" my undergraduate. At the age of 19, I became a graduate student and I learned a lot from my older colleagues.

At that time, the most important teacher for me was Schnirelman, a genius mathematician who died young. Then there are Kolmogorov, Lavrentiev, Plesner, Petrovsky, Pontriagin, Vinogradov, Lusternik, and they are all different. Some of them I like very much, and some of them, though I know they're very good, disagree —let me put it mildly—whose views (laughter). But they are all great mathematicians. I am very grateful to all of them and I have learned a lot from them.

Finally, I would like to give an example beyond mathematics, this short and concise sentence combines the other characteristics of simplicity, precision, etc. that I mentioned earlier. This is a quote from Nobel Laureate Isaac Bashevis Singer*: "As long as man destroys the weak with a knife and a gun, there can be no justice." ”

exegesis

*Sark Basheves Singer (1902–1991), Jewish-Polish, winner of the 1978 Nobel Prize in Literature, author of "Where the Rich Don't Die," "The Fire," "The Devil's Diary," short stories such as "The Fool's Golden Treasure," "Paradise in the Fool's Kingdom," children's books, and memoirs. The original text of this sentence is "There will be no justice as long as man will stand with a knife or with a gun and destroy those who are weaker than he is."

The text of this article is reproduced with permission from the WeChat public account "Hele Mathematics".

Special mention

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