Mathematical Fights...And in Corner 1....
If you are a student of any part of the fascinating history of mathematics, you are aware of "fights" or "strong disagreements" between mathematicians. The comparison between the people involved and the mathematics involved is also stark.
Hal Hellman's Great Feuds in Mathematics (2006) is eyeopening...ansd also an great introduction to the fascinating world of the history of mathematics.
Ten feuds are discussed and explored:
Tartaglia vs. Cardano (solving cubic equations)
Descartes vs. Fermat (analytic geometry and optics)
Newton vs. Leibniz (invention of calculus)
Bernoulli vs. Bernoullli (sibling rivalry)
Sylvester vs. Huxley (Ivory Tower vs. real world)
Kronecker vs. Cantor (infinity and set theory)
Borel vs. Zermelo (the "Nortorious Axiom")
Poincare vs. Russell (logical foundations of math)
Hilbert vs. Brouwer (Formalism vs. Intuitionism)
Absolujtists/Platonists vs. Fallibilists/Constructivists (dicovery vs. invention?)
These are a good starting set, though other feuds exist. They add senses of excitement, personality, and realism that seem to be missing from modern textbooks (or even old textbooks). That is, all of this that is fascinating gets "rinsed out" with the apparent goal being to provide a pallid view of mathematics.
If you like this sort of "tellall" text, Hellman has several related books out:
