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Jan 13, 2014 at 9:12 comment added John Stillwell It's even more surprising if you start with the inductive definitions of plus and times. The proof that $ab=ba$ comes as Proposition 72 in the first development of this theory, by Grassmann in 1861.
Dec 15, 2013 at 4:51 comment added Terry Tao Indeed, this fails in general when $a,b$ are ordinals.
S Dec 14, 2013 at 20:52 history answered Dan Petersen CC BY-SA 3.0
S Dec 14, 2013 at 20:52 history made wiki Post Made Community Wiki by Dan Petersen