Donald M. Davis (born 7 May 1945) is an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, p ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

specializing in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

. Davis received a B.S. from

MIT The Massachusetts Institute of Technology (MIT) is a private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

in 1967 and a PhD in mathematics at

Stanford Leland Stanford Junior University, commonly referred to as Stanford University, is a private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth governor of and th ...

in 1972, directed by

R. James Milgram Richard James Milgram (born 5 December 1939 in South Bend, Indiana) is an American mathematician, specializing in algebraic topology. He is the son of mathematician Arthur Milgram. Biography Milgram graduated from the University of Chicago with a ...

. After postdoctoral positions at

University of California, San Diego The University of California, San Diego (UC San Diego in communications material, formerly and colloquially UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California, United States. Es ...

and

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

, he began a 50-year career at

Lehigh University Lehigh University (LU), in Bethlehem, Pennsylvania, United States, is a private university, private research university. The university was established in 1865 by businessman Asa Packer. Lehigh University's undergraduate programs have been mixed ...

in 1974. In 2012 he was named an inaugural Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Since 2002, he has been Executive Editor of ''

Homology, Homotopy and Applications ''Homology, Homotopy and Applications'' is a peer-reviewed delayed open access mathematics journal published by International Press. It was established in 1999 and covers research on algebraic topology. The journal "Homology, Homotopy and Applic ...

''.

Research

Davis has published in

differential topology In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...

, topological robotics, and

combinatorial number theory In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Scope Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations (a ...

. He is an expert on immersions of projective spaces, and maintains a website with all known results for

real projective space In mathematics, real projective space, denoted or is the topological space of lines passing through the origin 0 in the real space It is a compact, smooth manifold of dimension , and is a special case of a Grassmannian space. Basic properti ...

s. He computed the

v_1

-periodic homotopy groups of all compact simple Lie groups.

Coaching

In 1993 Davis started the Lehigh Valley Math Team. In 2005, 2009, 2010, 2011, 2024 and 2025, they were national champions in the American Regions Math League (ARML). They have finished second or third in ARML seven other times. They won the Harvard/MIT Math Tournament (

HMMT HMMT is a semiannual (biannual) high school mathematics competition that started in 1998. The Autumn (November) tournament is held annually at Harvard University in Cambridge, Massachusetts, and the Spring (February) tournament is held annually at ...

) in 2023 and 2024, and the Princeton University Math Competition (PUMaC) in 2009, 2010, 2012, 2023, and 2024.

Running

From 1977 through 2009, Davis competed in marathon and ultramarathon races. He was the overall winner of ultramarathon races of 31 to 78 miles in the 1970s, 1980s, 1990s, and 2000s.

Selected publications

* This book was originally published by Princeton University Press in 1993. * *

Notes

External links

* at Lehigh University {{DEFAULTSORT:Davis, Donald 1945 births Living people 20th-century American mathematicians 21st-century American mathematicians Lehigh University faculty Fellows of the American Mathematical Society American topologists Massachusetts Institute of Technology alumni Stanford University alumni Mathematicians from Kentucky