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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
26
votes
Examples of conjectures that were widely believed to be true but later proved false
Borsuk's conjecture was believed to be true for 60 years till its counterexample was found in 1993 by Jeff Kahn and Gil Kalai.
They constructed an infinite family of counterexamples by using a result …
4
votes
Old books still used
"Projective Geometry" by Coxeter (1963), "Finite Geometries" by Dembowski (1968) and "Projective Planes" by Hughes and Piper (1973), still serve as great textbooks for these topics.