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

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- …
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 …
Cam McLeman's user avatar
  • 8,467
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 …
Cam McLeman's user avatar
  • 8,467
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, …
Cam McLeman's user avatar
  • 8,467