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Number Theory: In Context and Interactive

Karl-Dieter Crisman

References E.5 Historical References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 (Note that many of the other books referenced here have significant historical content, notably [E.4.5].)
[1]
Jim Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, (2005) (Website
 54 
www.cambridge.org/us/academic/subjects/mathematics/number-theory/elementary-number-theory-nine-chapters-2nd-edition?format=PB
)
Note.
Oodles of class-tested historical material and many, many exercises, including a welter of them on topics surrounding amicable numbers.
[2]
John J. Watkins, Number Theory: A Historical Approach, Princeton, (2013). (Website
 55 
press.princeton.edu/titles/10165.html
)
Note.
A very nice historically-oriented approach to elementary number theory. Includes Sage material in an appendix.
[3]
Oystein Ore, Number Theory and Its History, Dover, (1948). (Website
 56 
store.doverpublications.com/0486656209.html
)
Note.
Another conversational classic by Ore, with plenty of historical goodies.
[4]
Jay Goldman, The Queen of Mathematics, AK Peters, (1997) (Website
 57 
www.crcpress.com/The-Queen-of-Mathematics-A-Historically-Motivated-Guide-to-Number-Theory/Goldman/p/book/9781568810065
)
Note.
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.
[5]
William Dunham, Journey Through Genius, Wiley, (1990). (Website
 58 
www.wiley.com/WileyCDA/WileyTitle/productCd-0471500305.html
)
Note.
This is intended for those without calculus, but has many great number-theoretic bits all the same.
[6]
William Dunham, Euler: The Master of Us All, Mathematical Association of America, (1999). (Website
 59 
www.maa.org/press/books/euler-the-master-of-us-all
)
Note.
This book has some nice discussion of Euler’s number theory alongside many other historical vignettes with real math power.
[7]
A. Knoebel et al., Mathematical Masterpieces: Further Chronicles by the Explorers, Springer, (2007). (Website
 60 
www.springer.com/us/book/9780387330600
)
Note.
Collection of additional classroom resources focused on primary source material, including the Basel problem and quadratic reciprocity.
[8]
André Weil, Number Theory: An approach through history From Hammurapi to Legendre, Birkhäuser, (1984). (Website
 61 
www.springer.com/la/book/9780817645656#reviews
)
Note.
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.
[9]
Waclaw Sierpínski, Pythagorean Triangles, Dover, (2013). (Website
 62 
store.doverpublications.com/0486174832.html
)
Note.
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’.
[10]
Ulrich Libbrecht, Chinese Mathematics in the Thirteenth Century, Dover, (1973). (No website)
Note.
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.
[11]
Alireza Djafari Naini, Geschichte der Zahlentheorie im Orient, Verlag Klose und Co., (1982). (No website)
Note.
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.
[12]
Paul M. Nahin, In Pursuit of Zeta-3: The World’s Most Mysterious Unsolved Math Problem, Princeton, (2021). (Website
 63 
press.princeton.edu/books/hardcover/9780691206073/in-pursuit-of-zeta-3
)
Note.
More information than you would ever want to know about Apéry’s constant, by an engaging author. Many computations.
[13]
David Pengelley, Number Theory Through the Eyes of Sophie Germain: An Inquiry Course, Mathematical Association of America, (2023). (Website
 64 
bookstore.ams.org/view?ProductCode=CLRM/70
)
Note.
This book really fits under several categories. If you are interested in using an inquiry-based pedagogy, have fairly well-prepared students, and are interested in using primary sources to explore number theory with them, why not explore with one of the greats, Sophie Germain? Early reviews (such as this one
 65 
maa.org/press/maa-reviews/number-theory-through-the-eyes-of-sophie-germain
) have been laudatory.
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