Harold Mortimer Edwards, Jr. (August 6, 1936 – November 10, 2020) was an American mathematician working in
number theory,
algebra, and the history and philosophy of mathematics.
Higher Arithmetic: An Algorithmic Introduction to Number Theory (2008)[8] An extension of Edwards' work in Essays in Constructive Mathematics, this textbook covers the material of a typical undergraduate
number theory course,[9] but follows a
constructivist viewpoint in focusing on
algorithms for solving problems rather than allowing purely existential solutions.[9][10] The constructions are intended to be simple and straightforward, rather than efficient, so, unlike works on
algorithmic number theory, there is no analysis of how efficient they are in terms of their
running time.[10]
Essays in Constructive Mathematics (2005)[11] Although motivated in part by the history and philosophy of mathematics, the main goal of this book is to show that advanced mathematics such as the
fundamental theorem of algebra, the theory of
binary quadratic forms, and the
Riemann–Roch theorem can be handled in a constructivist framework.[12][13][14] The second edition (2022) adds a new set of essays that reflect and expand upon the first.[15] This was Edwards' final book, finished shortly before his death.[16]
Linear Algebra, Birkhäuser, (1995)
Divisor Theory (1990)[17] Algebraic divisors were introduced by Kronecker as an alternative to the theory of
ideals.[18] According to the citation for Edwards' Whiteman Prize, this book completes the work of Kronecker by providing "the sort of systematic and coherent exposition of divisor theory that Kronecker himself was never able to achieve."[5]
Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (1977)[23] As the word "genetic" in the title implies, this book on
Fermat's Last Theorem is organized in terms of the origins and historical development of the subject. It was written some years prior to
Wiles' proof of the theorem, and covers research related to the theorem only up to the work of
Ernst Kummer, who used
p-adic numbers and
ideal theory to prove the theorem for a large class of exponents, the
regular primes.[24][25]
Riemann's Zeta Function (1974)[26] This book concerns the
Riemann zeta function and the
Riemann hypothesis on the location of the zeros of this function. It includes a translation of Riemann's original paper on these subjects, and analyzes this paper in depth; it also covers methods of computing the function such as
Euler–Maclaurin summation and the
Riemann–Siegel formula. However, it omits related research on other
zeta functions with analogous properties to Riemann's function, as well as more recent work on the
large sieve and density estimates.[27][28][29]
^Graduate Texts in Mathematics 50, Springer-Verlag, New York, 1977,
ISBN0-387-90230-9. Reprinted with corrections, 1996,
ISBN978-0-387-95002-0,
MR1416327. Russian translation by V. L. Kalinin and A. I. Skopin. Mir, Moscow, 1980,
MR0616636.
^Review by Charles J. Parry (1981), Bulletin of the AMS4 (2): 218–222.