Wilbur Richard Knorr (August 29, 1945 – March 18, 1997) was an American
historian of mathematics and a professor in the departments of philosophy and classics at
Stanford University. He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century.[1]
Knorr was a talented violinist, and played first violin in the Harvard Orchestra, but he gave up his music when he came to Stanford, as the pressures of the tenure process did not allow him adequate practice time.[1][3]
Books
The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry.[5]
This work incorporates Knorr's Ph.D. thesis. It traces the early history of
irrational numbers from their first discovery (in
Thebes between 430 and 410 BC, Knorr speculates), through the work of
Theodorus of Cyrene, who showed the irrationality of the square roots of the integers up to 17, and Theodorus' student
Theaetetus, who showed that all non-square integers have irrational square roots. Knorr reconstructs an argument based on
Pythagorean triples and
parity that matches the story in
Plato's Theaetetus of Theodorus' difficulties with the number 17, and shows that switching from parity to a different dichotomy in terms of whether a number is square or not was the key to Theaetetus' success. Theaetetus classified the known irrational numbers into three types, based on analogies to the
geometric mean,
arithmetic mean, and
harmonic mean, and this classification was then greatly extended by
Eudoxus of Cnidus; Knorr speculates that this extension stemmed out of Eudoxus' studies of the
golden section.[1][3][6][7]
Along with this history of irrational numbers, Knorr reaches several conclusions about the history of
Euclid's
Elements and of other related mathematical documents; in particular, he ascribes the origin of the material in Books 1, 3, and 6 of the Elements to the time of
Hippocrates of Chios, and of the material in books 2, 4, 10, and 13 to the later period of Theodorus, Theaetetus, and Eudoxos. However, this suggested history has been criticized by
van der Waerden, who believed that books 1 through 4 were largely due to the much earlier
Pythagorean school.[8]
Ancient Sources of the Medieval Tradition of Mechanics: Greek, Arabic, and Latin studies of the balance.[9]
This book, aimed at a general audience, examines the history of three classical problems from
Greek mathematics:
doubling the cube,
squaring the circle, and
angle trisection. It is now known that none of these problems can be solved by
compass and straightedge, but Knorr argues that emphasizing these impossibility results is an anachronism due in part to the
foundational crisis in 1930s mathematics.[11] Instead, Knorr argues, the Greek mathematicians were primarily interested in how to solve these problems by whatever means they could, and viewed theorem and proofs as tools for problem-solving more than as ends in their own right.[1]
Textual Studies in Ancient and Medieval Geometry.[12]
This is a longer and more technical "appendix" to The Ancient Tradition of Geometric Problems in which Knorr examines the similarities and differences between ancient mathematical texts carefully in order to determine how they influenced each other and untangle their editorial history.[1][11] One of Knorr's more provocative speculations in this work is that
Hypatia may have played a role in editing
Archimedes' Measurement of a Circle.[3]
^Unguru, Sabetai (1977), "Incommensurability and irrationality: A new historical interpretation", History of Science, 15: 216–227,
doi:
10.1177/007327537701500303,
S2CID220854110. Although published as a regular paper, this is an extended review of The Evolution of the Euclidean Elements, for which Unguru's review in Isis is a precis.
^
abReview of both The Ancient Tradition of Geometric Problems and Textual Studies in Ancient and Medieval Geometry by Thomas Drucker (1991), Isis82: 718–720,
doi:
10.1086/355947.