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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 …

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 …

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 …

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 …

It may be that certain theorems, when proved true, counterintuitively retard progress in certain domains. Lloyd Trefethen provides two examples: Faber's Theorem on polynomial interpolation: Interpre …

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 …

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 …

The title is a quote from a Jim Holt article entitled, "The Riemann zeta conjecture and the laughter of the primes" (p. 47).1 His example of a "long-standing conjecture" is the Riemann hypothesis, and …

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 …

Does anyone know when and why the Fraktur script was introduced for Lie and other algebras—$\mathfrak{g}$, $\mathfrak{gl}_n$, $X/\mathfrak{g}$, $\mathfrak{g}\oplus\mathfrak{g}$, $\mathfrak{su}$, $\mat …

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 …

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 …

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. …

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 …

Q. When did the notion of homeomorphism reach its modern formulation as a bicontinuous bijection, i.e., a continuous bijection between topological spaces whose inverse is also continuous? …