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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 …