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Mathematics: Its Content, Methods and Meaning

old.maa.org

21–30 of 47 posts

Re: Mathematics: Its Content, Methods and Meaning

#21
post #17

This is a great book if you already know good amount of Math. It helps you fit things into a bigger picture. Really appreciate the fact that something like this exists.

FWIW the Preface says it's written for people with secondary school mathematics education - whatever that meant in the Soviet Union in the 1950s.

Soviet primary and secondary education on math was one of the few good things of the regime.

Culturally, mastery of mathematics, engineering, chess and technical inteligence were a source of social status and prestige.

Yes, an engineer could have been badly paid, he was not free in a liberal sense, be subject to the vagaries of political paranoia waves, but he commanded a certain level of social respect that even good paid engineers in the sillicon valley can hardly imagine. A soviet physicist could be underpaid and constrained by bureaucracy, but being introduced by your parents as a professor of the Keldysh Institute of Applied Mathematics or the Steklov Mathematical Institute in your home town give you almost an aura. Kids would look at you and dream of being admitted to secondary institutions like Kolmogorov's boarding school at the Moscow State University.

Given that, it was as likely for people in political positions of power to have a good mathematical background as it is to find a lawyer in the US Capitol.

Re: Mathematics: Its Content, Methods and Meaning

#22
This book is really fascinating because it contains a surprising amount of Soviet ideology. The authors repeatedly state that mathematics is posterior to the material world, not prior to it. That is, mathematics is just the observation of regularity in the world, particularly those discovered by people working to create things. Contrast this with the still heavily idealistic world of western mathematics, where mathematicians are more likely to sympathize with the notion that numbers are real things somewhere out there whose structures the real world supervenes upon in some way.

Interesting stuff!

Even though I favor the Soviet view of mathematics personally (I do not think numbers "exist" out there independent of the material world), I think this approach hampers the didactic goals of the text and probably hurt Soviet mathematics as well. The examples in the text are all highly concrete (literally things like rubber mats when discussing curvature). This very down to earth style makes the abstract notions of curvature in other contexts (for example, general relativity) more difficult to grasp, in my opinion.

On the other hand, some people prefer strong, material, examples of mathematical ideas. This book definitely provides that. The section on affine maps in terms of fixing the plane of a surveillance airplane photograph is beautifully concrete.

Re: Mathematics: Its Content, Methods and Meaning

#24
post #17

This is a great book if you already know good amount of Math. It helps you fit things into a bigger picture. Really appreciate the fact that something like this exists.

FWIW the Preface says it's written for people with secondary school mathematics education - whatever that meant in the Soviet Union in the 1950s.

Right. The book is accessible to a smart student in grades 9-10 and most everybody in grades 11-12.

Re: Mathematics: Its Content, Methods and Meaning

#25
post #17

Earlier quoted context omitted.

FWIW the Preface says it's written for people with secondary school mathematics education - whatever that meant in the Soviet Union in the 1950s.

Soviet primary and secondary education on math was one of the few good things of the regime. Culturally, mastery of mathematics, engineering, chess and technical inteligence were a source of social status and prestige. Yes, an engineer could have been badly paid, he was not free in a liberal sense, be subject to the vagaries of political paranoia waves, but he commanded a certain level of social respect that even goo…

> Culturally, mastery of mathematics, engineering, chess and technical intelligence were a source of social status and prestige.

This is what has severely degraded in current-day global society/culture and due to globalization exported everywhere.

However, Soviet-era Science/Mathematics books are still highly regarded/prized in many countries by the older generation.

Re: Mathematics: Its Content, Methods and Meaning

#26

This book is really fascinating because it contains a surprising amount of Soviet ideology. The authors repeatedly state that mathematics is posterior to the material world, not prior to it. That is, mathematics is just the observation of regularity in the world, particularly those discovered by people working to create things. Contrast this with the still heavily idealistic world of western mathematics, where mathem…

In this context, people should also read;

On Teaching Mathematics by V.I.Arnold - https://archive-dsweb.siam.org/The-Magazine/All-Issues/vi-ar...

Mathematics and Physics: mother and daughter or sisters? by V.I.Arnold - https://ufn.ru/en/articles/1999/12/c/

Re: Mathematics: Its Content, Methods and Meaning

#27
post #23
post #18

Where can I find mathematical book titles like this one?

Look for books from "Mir publishers", there are some nice soviet books. https://mirtitles.org/tag/mathematics/

Very very cool! Somehow most names are unfamiliar.

I have very much enjoyed the OP (Mathematics: Its Content, Methods and Meaning). Any particular books that you would recommend?

Re: Mathematics: Its Content, Methods and Meaning

#29
post #27
post #23

Earlier quoted context omitted.

Look for books from "Mir publishers", there are some nice soviet books. https://mirtitles.org/tag/mathematics/

Very very cool! Somehow most names are unfamiliar. I have very much enjoyed the OP (Mathematics: Its Content, Methods and Meaning). Any particular books that you would recommend?

Not the person you asked the question of;

I thought everybody knew of this site especially Indians since it was started and is lovingly maintained by an Indian :-) A lot of hard work has gone into it with not just scanning of the books but also typesetting some of them in latex for better rendering and reading. The website author deserves all the credit/acclaim he can get.

All of the books are hosted on internet archive which you can browse here - https://archive.org/details/mir-titles

Many of the titles are also published in hard copy form by low-cost Indian publishers on Amazon India.

Some recommendations which are not typical textbooks;

1) Little Mathematics Library series - https://mirtitles.org/2024/05/11/little-mathematics-library-...

2) Books by Lev Tarasov. Some of these books are structured as a dialogue and thus walks you through the conceptual process. Titles are on Calculus, Probability, Quantum Mechanics, Physics Q/A etc. All worth reading; some of them are latex remastered versions - https://mirtitles.org/?s=Tarasov

3) Higher Math for Beginners(with Yaglom) and Elements of Applied Mathematics(with Myskis) by Zeldovich - https://mirtitles.org/?s=zeldovich

4) Mathematical Handbook (two vols); Elementary Mathematics and Higher Mathematics by M.Vygodsky. - https://mirtitles.org/?s=vygodsky

5) Handbook of Physics by Yavorsky and Detlaf - https://mirtitles.org/?s=Handbook+of+Physics

6) Fundamentals of Physics by Ivanov - https://mirtitles.org/2018/04/21/fundamentals-of-physics-iva...

7) Ever popular Science/Maths books by Yakov Perelman viz. Physics for Entertainment, Mathematics can be Fun etc. - https://mirtitles.org/?s=Yakov+Perelman

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