Appendix B List of Historical Remarks
For convenience, below we collect some of the short historical remarks in the text. We hope these, and the many places where the history was part and parcel of the main text, whetted the reader’s appetite for more investigations!
There is a huge number of places to learn about the history of number theory – including many of the books and articles in the References and Further Resources, especially the Historical References. Another excellent compendium of resources about mathematics history more generally is the MacTutor 1 site.
Historical remark 2.3.2 Euclid’s Elements
Historical remark 2.4.7 Bezout and friends
Historical remark 3.1.1 Diophantine and his equations
Historical remark 3.5.2 Bachet de Méziriac
Historical remark 3.5.3 Bachet equation
Historical remark 3.5.6 Catalan’s conjecture – solved
Historical remark 5.3.3 Ancient Chinese work on remainders
Historical remark 6.2.5 Eratosthenes
Historical remark 7.2.4 Hensel’s Lemma
Historical remark 11.3.5 Diffie and Hellman
Historical remark 11.4.1 Diffie-Hellman controversy
Historical remark 11.5.2 Who is RSA?
Historical remark 11.6.2 Sophie Germain
Historical remark 12.1.5 Marin Mersenne
Historical remark 12.1.7 GIMPS
Historical remark 12.1.8 The Skylake bug
Historical remark 12.6.7 Factoring Fermat
Historical remark 13.0.2 Albert Girard
Historical remark 13.0.3 Leonhard Euler
Historical remark 13.0.4 Pierre de Fermat
Historical remark 13.1.8 Fibonacci
Historical remark 13.4.16 Hermann Minkowski
Historical remark 14.1.3 Carl Friedrich Gauss
Historical remark 15.3.2 Louis Mordell
Historical remark 15.5.6 Brahmagupta
Historical remark 15.5.7 Stigler’s Law
Historical remark 16.3.7 Joseph-Louis Lagrange
Historical remark 16.4.1 Adrien-Marie Legendre
Historical remark 17.2.1 Gotthold Eisenstein
Historical remark 19.4.13 Thabit ibn Qurra
Historical remark 21.2.7 Skewes’ Number
Historical remark 21.3.2 The Prime Number Theorem
Historical remark 21.3.3 Pafnuty Chebyshev
Historical remark 22.2.2 Lejeune Dirichlet
Historical remark 22.3.9 The Pentium bug
Historical remark 22.3.10 Twin prime status
Historical remark 23.1.2 August Möbius
Historical remark 24.2.3 Bernhard Riemann
mathshistory.st-andrews.ac.uk
