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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

9 votes
2 answers
2k views

Who first defined quantum integers?

Who first gave the definition of quantum integers $$ [m]_q = \frac{1 - q^m}{1 - q} $$ and addition as $$ [m]_q \oplus_q [n]_q = [m]_q + q^m [n]_q $$ and multiplication as $$ [m]_q \otimes_q [n]_q = …
Martin Peters's user avatar
4 votes

Looking for Arnol'd quote about Russian students vs western mathematicians

Maybe you are referring to his book with problems for schoolchildren? See problem 13 there, and also a remark in the preface.
Martin Peters's user avatar
1 vote

History of the Sampling Theorem

Some background on Kotelnikov's contribution is given in A G Vitushkin: Half a Century As One Day in the book Bolibruch, Osipov, Sinai (Editors): Mathematical Events of the Twentieth Century and also …
Martin Peters's user avatar
7 votes

Mathematicians with both “very abstract” and “very applied” achievements

There is Ernst Zermelo, who is well-known for his work in logic, but who was also a pioneer in optimisation and what is now called control theory.
7 votes

Autobiographies of mathematicians

An outstanding autobiography in my opinion is Egon Balas: Will to Freedom.
2 votes

Insightful books about elementary mathematics

Two great ones are: Fuchs, Tabachnikov: Mathematical Omnibus and Arnold: Lectures and Problems: A Gift to Young Mathematicians.
3 votes

History of ODE and PDE reference request

You might consider reading Hairer, Wanner: Analysis by Its History, which includes differential equations in its treatment, and Bertil Gustafsson Scientific Computing which focuses on the history of c …
Martin Peters's user avatar