Dr. Gaebler in front of a blackboard, teaching class.

David Gaebler

Associate Professor of Mathematics
"The poetry of mathematics involves looking at old ideas in new ways and making unexpected connections between apparently disparate concepts."
— David Gaebler

Faculty Information

Additional Faculty Information for David Gaebler


B.S., Mathematics and Physics, Harvey Mudd College, 2004

M.A., Biblical Studies, Westminster Seminary California, 2006

M.A., Mathematics, UCLA, 2008

Ph.D., Mathematics, University of Iowa, 2013


Honorable Mention on USA Mathematical Olympiad (top 17 nationally), 1999

Honorable Mention on William Lowell Putnam Mathematics Competition (ranked 46th and 40th nationally), 2000 and 2003

Harvey Mudd College Robert James Prize (awarded to two rising sophomores who excel in mathematics), 2001

Harvey Mudd College Giovanni Borelli Mathematics Prize (awarded to a rising senior or seniors with outstanding achievement and potential), 2003


NSF Graduate Research Fellowship, 2006-2009

University of Iowa Outstanding Teaching Assistant Award (awarded to 30 annually from all university departments)

Bor-Luh Lin Award for Outstanding Thesis in Mathematics, University of Iowa, 2013

D.C. Spriestersbach Prize for Outstanding Dissertation in Mathematics, Engineering, and the Physical Sciences, University of Iowa, 2012-2013


“A combinatorial approach to hyperharmonic numbers”
Arthur T. Benjamin, David Gaebler, and Robert Gaebler, Integers 3 (2003), 9 pp.

“Toeplitz operators on locally compact abelian groups”
David Gaebler, undergraduate thesis, 2004.

“Unital dilations of completely positive semigroups”
David Gaebler, Ph. D. thesis, 2013.

“Continuous unital dilations of completely positive semigroups”
David J. Gaebler, Journal of Functional Analysis 269 (2015) no. 4, 998-1027.


Education is more than skill training. It includes reflection and contemplation and should ultimately engage the heart as well as the mind, leading us to rejoice in the wonders of the physical world, of human civilization, and of the divine attributes. “Great are the works of the Lord, studied by all who delight in them” (Psalm 111:2).

Initially, the lure of mathematics was all about the thrill of the chase: the challenge of a difficult problem and the rush that comes from solving it. Further in my development, I became impressed by the power of mathematical abstraction and its ability to, in the words of Fourier, “compare the most diverse phenomena and discover the secret analogies that unite them.”

As everyone knows, mathematics requires years of patient toil in order to develop a set of tools. But the point of learning the grammar is that you can then go on and read poetry!

The poetry of mathematics involves looking at old ideas in new ways and making unexpected connections between apparently disparate concepts. It involves a dance between intuition and rigor, as the flash of insight that solves a problem is followed by the careful deduction that verifies the insight and communicates it to others.

Teaching mathematics means teaching students to perform a sequence of tasks, but also to think mathematically—not only to solve a problem but to think about how it relates to other problems, and about why they are lucky enough that the problem turned out to be solvable in the first place.

Hillsdale is a community of scholars who delve deeply into the best that has been thought and said, and who are excited by the pursuit of truth. Most of our mathematics majors are double majors—some in obviously related disciplines like physics or economics, but others in far-reaching areas like history and art and philosophy and German.

At Hillsdale, you will find mathematics professors who appreciate the humanities, and humanities professors who appreciate mathematics.

Outside the world of mathematics, listening to, practicing, and performing music are among my greatest joys. I also enjoy board and card games—Axis & Allies and bridge are the respective favorites, but I’ve rarely met a game I didn’t like. I read a little of a lot of things. Most of all, though, my family fills my downtime, whether we’re busy at play or sitting quietly by the fireplace and enjoying each other’s company.