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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
7
votes
Autobiographies of mathematicians
Edward Frenkel's "Love and Math" is a mix of popular maths book, autobiography, and general declaration of love towards mathematics.
3
votes
Autobiographies and correspondences of mathematicians
I think you will enjoy Norbert Wiener's autobiographic "I Am a Mathematician".
3
votes
Autobiographies and correspondences of mathematicians
Edward Frenkel's "Love and Math" is a mix of popular maths book, autobiography, and general declaration of love towards mathematics.
6
votes
The parity conjecture
Let me add a few remarks to the very nice CW answer already given.
The parity conjecture (i.e. algebraic rank equals analytic rank modulo 2) is known for all elliptic curves over number fields (not …