Skip to main content
Logo image

References E.5 Historical References

Number Theory is also a very old field, as should be clear from using this book. Here I have collated references intended both for mathematicians and the fabled ‘educated laity’. (Note that many of the other books referenced here have significant historical content, notably [E.4.5].)
Jim Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, (2005) (Website 54 )
Oodles of class-tested historical material and many, many exercises, including a welter of them on topics surrounding amicable numbers.
John J. Watkins, Number Theory: A Historical Approach, Princeton, (2013). (Website 55 )
A very nice historically-oriented approach to elementary number theory. Includes Sage material in an appendix.
Oystein Ore, Number Theory and Its History, Dover, (1948). (Website 56 )
Another conversational classic by Ore, with plenty of historical goodies.
Jay Goldman, The Queen of Mathematics, AK Peters, (1997) (Website 57 )
A truly historical sojourn through much of number theory up through the early twentieth century, with extensive primary source material and investigation of Gauss’ monumental work. Sadly, largely beyond the level of this text.
William Dunham, Journey Through Genius, Wiley, (1990). (Website 58 )
This is intended for those without calculus, but has many great number-theoretic bits all the same.
William Dunham, Euler: The Master of Us All, Mathematical Association of America, (1999). (Website 59 )
This book has some nice discussion of Euler’s number theory alongside many other historical vignettes with real math power.
A. Knoebel et al., Mathematical Masterpieces: Further Chronicles by the Explorers, Springer, (2007). (Website 60 )
Collection of additional classroom resources focused on primary source material, including the Basel problem and quadratic reciprocity.
André Weil, Number Theory: An approach through history From Hammurapi to Legendre, Birkhäuser, (1984). (Website 61 )
Absolutely first-rate mathematician’s insider view into the contributions of Fermat and Euler. Plenty of opinions and connections to modern mathematics, though sadly it will never be updated to connect Wiles’ work on elliptic curves to Fermat’s legacy.
Waclaw Sierpínski, Pythagorean Triangles, Dover, (2013). (Website 62 )
In general it’s accessible to a student using this book, though as a reprint of a fifty-year-old book it (as a recent College Mathematics Journal review put it) could use ‘certain updates’.
Ulrich Libbrecht, Chinese Mathematics in the Thirteenth Century, Dover, (1973). (No website)
Reprint of MIT Press original publication (now out of print), an extremely thorough discussion of Qin Jiushao’s entire mathematical opus within its cultural context. About half the book is a monograph on the Chinese Remainder Theorem, hence its inclusion in this set of references.
Alireza Djafari Naini, Geschichte der Zahlentheorie im Orient, Verlag Klose und Co., (1982). (No website)
Special focus on number theory in the medieval era in the Islamic world, especially Persian mathematicians. Many explicit examples, and comparisons with Diophantus and more modern sources.
Paul M. Nahin, In Pursuit of Zeta-3: The World’s Most Mysterious Unsolved Math Problem, Princeton, (2021). (Website 63 )
More information than you would ever want to know about Apéry’s constant, by an engaging author. Many computations.