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

110 votes
10 answers
30k views

What is the oldest open problem in mathematics?

What is the oldest open problem in mathematics? By old, I am referring to the date the problem was stated. Browsing Wikipedia list of open problems, it seems that the Goldbach conjecture (1742, every …
11 votes
2 answers
1k views

Early successes of Schwartz distribution theory

What are the early successes of Schwartz distributions theory? What are the hard theorems that became simple and what open problems were solved with this new tool soon after Laurent Schwartz released …
27 votes
8 answers
13k views

The $2\pi$ in the definition of the Fourier transform

There are several conventions for the definition of the Fourier transform on the real line. 1 . No $2\pi$. Fourier (with cosine/sine), Hörmander, Katznelson, Folland. $ \int_{\bf R} f(x) e^{-ix\xi} …
7 votes
1 answer
791 views

author of a paradoxical decomposition of the interval

I am looking for the original author and the date of publication of the following result. Theorem There exist subsets $E_i\subset [0,1)$, $i\in {\bf Z}$, pairwise disjoints and real numbers $a_i$ suc …