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

36 votes
35 answers
11k views

Titles composed entirely of math symbols

I apologize for burdening MO with such a vapid, nonresearch question, but I have been curious ever since Suvrit's popular October 2010 Most memorable titles MO question if there were any "$E=mc^2$-tit …
67 votes
16 answers
9k views

What do named "tricks" share?

There are a number of theorems or lemmas or mathematical ideas that come to be known as eponymous tricks, a term which in this context is in no sense derogatory. Here is a list of 11 such tricks (the …
25 votes
3 answers
12k views

Why is a ring called a "ring"?

Why is a ring called "ring" (or Zahlring in German)? There seems to (naive) me nothing more ring-like to a ring than there is to a group or a field. I am particularly interested to learn why the wor …
236 votes
36 answers
35k views

Conway's lesser-known results

John Horton Conway is known for many achievements: Life, the three sporadic groups in the "Conway constellation," surreal numbers, his "Look-and-Say" sequence analysis, the Conway-Schneeberger $15$-th …
11 votes
3 answers
846 views

Dehn's solution to Hilbert's 3rd: 1901 or 1902?

This is a simple bibliographic request that I have been unable to pin down. Max Dehn's solution to Hilbert's 3rd problem is: Max Dehn, "Über den Rauminhalt." Mathematische Annalen 55 (190x), no. 3, …
103 votes
15 answers
17k views

Have you solved problems in your sleep?

I have hit upon major (for me—relative to my trivial accomplishments) insights in my research in various sleep-deprived altered states of consciousness, e.g., long solo car-drives extending through th …
8 votes
0 answers
541 views

Landau's century-old problems: Anything comparable?

Landau's four problems are now over a century old (1912), and each still unsolved. This seems remarkable, even though he was not the originating author all four (maybe only the 4th?). Still, he isolat …
11 votes
2 answers
2k views

Great polyhedra: What does "great" signify?

Great Cubicuboctahedron Great Icosacronic Hexecontahedron Great Rhombic Triacontahedron Great Snub Icosidodecahedron Great Stellated Dodecahedron Great Triakis Octahedron ... There are many polyhedr …
123 votes
35 answers
18k views

Rediscovery of lost mathematics

Archimedes (ca. 287-212BC) described what are now known as the 13 Archimedean solids in a lost work, later mentioned by Pappus. But it awaited Kepler (1619) for the 13 semiregular polyhedra to be rec …
67 votes
22 answers
10k views

When has discrete understanding preceded continuous?

From my limited perspective, it appears that the understanding of a mathematical phenomenon has usually been achieved, historically, in a continuous setting before it was fully explored in a discrete …
25 votes
4 answers
2k views

History of powers beyond squares and cubes

The ancient Babylonians understood squares:       Plimpton 322 The ancient Athenians understood cubes, if we can take doubling the cube, i.e., the Delian problem, as evidence. My question is: Q. …
15 votes
1 answer
1k views

Gauss-Bonnet Theorem: Neither Gauss nor Bonnet [closed]

Tristan Needham says (p.174),* "While Gauss and Bonnet certainly paved the road to [the Gauss-Bonnet Theorem], neither one of them was even aware of this extraordinary result, let alone stated it!" …
25 votes
2 answers
2k views

Who first dubbed them "expander graphs"?

Expander graphs ("sparse graphs that have strong connectivity properties") burst onto the mathematical scene around the millennium, but I have not been successful in tracing the origin of (a) the conc …
31 votes
1 answer
5k views

Why do we use $\varepsilon$ and $\delta$?

My understanding (from a talk by Rob Bradley) is that Cauchy is responsible for the now-standard $\varepsilon{-}\delta$ formulation of calculus, introduced in his 1821 Cours d’analyse. Although perha …
140 votes
7 answers
34k views

Is the boundary $\partial S$ analogous to a derivative?

Without prethought, I mentioned in class once that the reason the symbol $\partial$ is used to represent the boundary operator in topology is that its behavior is akin to a derivative. But after refle …

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