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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
12
votes
Which mathematical ideas have done most to change history?
Can you say something about the audience of this course? Popular math? Undergrads? grads? That might set some appropriate response parameters.
If this were a graduate-level course (I suspect not, …
11
votes
Accepted
sums of rational squares
This result is pretty shy of needing the full Hasse-Minkowski Theorem. Indeed, since Fermat already knew which integers were a sum of two integer squares, it would suffice for him to show that those …
26
votes
2
answers
2k
views
William Rowan Hamilton and Algebra as Time
This question ended up longer than I intended (though most of the bulk is interesting remarks by Hamilton), so I thought it might be good to include my question at the beginning before the admittedly- …
2
votes
Equivalent definitions of Gaussian curvature
Chapter 3 ("The Geometry of the Gauss Map") of Do Carmo's "Differential Geometry of Curves and Surfaces" has a very nice discussion along these lines, though I don't remember much historical backgroun …