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A long-standing conjecture in Number Theory is that for each positive integer $n$ there is no stretch of $n$ consecutive integers containing more primes than the stretch from 2 to $n+1$. Just looking …

Maybe I've missed it, but it seems no one has mentioned Pascal's triangle. According to Wikipedia it had a slew of earlier discoverers, going back to "The Persian mathematician Al-Karaji (953–1029) [w …

In 1917, Schur showed that there was no hope of proving Fermat's Last Theorem by ruling out the corresponding congruences. He applied a result from Ramsey Theory, but of course Ramsey Theory had not y …

"Has anybody quoted that passage in this meaning later?" Does this qualify? Jennifer Geldard - Torch songs: Ambition, distraction, uglification, and derision

Quoting https://en.wikipedia.org/wiki/Ax%E2%80%93Kochen_theorem, "The Ax–Kochen theorem, named for James Ax and Simon B. Kochen, states that for each positive integer $d$ there is a finite set $Y_d$ o …

John McCleary will give a talk at the JMM in a couple of weeks on "Hassler Whitney and Fire Control in WWII." Whitney "was assigned to work on fire control, the mathematics of aiming weapons for accur …

The nonzero characteristics of fields are precisely the prime numbers.

The abelian simple groups are precisely the groups of prime order.

Eric Temple Bell, The Development of Mathematics, page 76: "Like Euclid in his explicit statement of the parallel postulate, Archimedes had the true mathematician's caution in the presence of the obvi …

There are stories about work of Banach being written up by people other than Banach. Details and debunking links available on another MO thread, Who wrote up Banach's Thesis?

Albert Gloden's book, Mehrgradige Gleichungen, was published in Groningen in 1944. Some of it is out of date, but it's still a good place to start the study of multigrade equations (equations in integ …

According to Branko Grunbaum, An enduring error, Elemente der Mathematik 64 (2009) 89-101, reprinted in Mircea Pitici, ed., The Best Writing On Mathematics 2010, Andreini in 1905 claimed that there ar …

According to Branko Grunbaum, An enduring error, Elemente der Mathematik 64 (2009) 89-101, reprinted in Mircea Pitici, ed., The Best Writing On Mathematics 2010, Daublebsky in 1895 found that there ar …

Another one from Grunbaum's paper: According to Branko Grunbaum, An enduring error, Elemente der Mathematik 64 (2009) 89-101, reprinted in Mircea Pitici, ed., The Best Writing On Mathematics 2010, Bru …

A Group of Order 8,315,553,613,086,720,000 by J H Conway, Bull. London Math. Soc. (1969) 1 (1): 79-88, https://doi.org/10.1112/blms/1.1.79 Maybe it's cheating to call this memorable - I remembered the …