Michael Kinyon


What I do

Professor of Mathematics

Professional Biography

I earned my BS, MS and PhD degrees from the University of Utah in 1986, 1988 and 1991, respectively. From 1992 to 2006, I was a professor at Indiana University South Bend. I have been a professor at DU since 2006. I am also adjunct full professor at the Open University of Portugal and a full member of the Center for Experimental and Stochastic Mathematics of the University of Lisbon.


  • Ph.D., Mathematics, University of Utah, 1991
  • MS, Mathematics, University of Utah, 1988
  • BS, Mathematics, University of Utah, 1986

Professional Affiliations

  • American Mathematical Society


My research specialty is algebra, especially quasigroups/loops and semigroups/monoids. I am especially interested in the use of automated deduction in mathematics. Most of what I do involves coaxing computers into proving theorems for me.

Key Projects

  • Moufang Semiloops
  • Fourth Mile High Conference on Nonassociative Mathematics
  • 3rd Mile High Conference on Nonassociative Mathematics

Featured Publications

  • The structure of automorphic loops
  • Conjugacy in inverse semigroups
  • Four notions of conjugacy for abstract semigroups
  • Proof simplification and automated theorem proving
  • Decidability and independence of conjugacy problems in finitely presented monoids


  • Loops and the AIM Conjecture: History and Progress
  • Automorphic loops and their associated permutation groups
  • Loops and their multiplication groups
  • Proof simplification and Prover9
  • Nonassociative right hoops


  • United Methodist Church University of Denver Teacher/Scholar of the Year 2013, United Methodist Church/University of Denver
  • Pedro Nunes Award for Excellence in Online Teaching, Universidad Aberta