Michael Kinyon


What I do

Professor of Mathematics


quasigroups, semigroups, automated deduction

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.

Areas of Research

quasigroups and loops
semigroups and monoids
noncommutative lattices
and applications of automated deduction to all of the above

Key Projects

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

Featured Publications

Kinyon, M., Kunen, K., Phillips, J. D., & Vojtechovsky, P. (2014). The structure of automorphic loops. Transactions of the American Mathematical Society.
Araujo, J., Kinyon, M., Konieczny, J., & Malheiro, A. (2017). Four notions of conjugacy for abstract semigroups. Mathematical Proceedings of the Cambridge Philosophical Society, 147(6), 1169-1214.
Kinyon, M. (2019). Proof simplification and automated theorem proving. Philosophical Transactions of the Royal Society A.: Mathematical, Physical and Engineering Sciences, 377(2140), 9.
Araujo, J., Kinyon, M., Konieczny, J., & Malheiro, A. (2018). Decidability and independence of conjugacy problems in finitely presented monoids. Theoretical Computer Science , 731, 88-98.


Kinyon, M. (2016). Loops and the AIM Conjecture: History and Progress. 1st Conference on Artificial Intelligence and Theorem Proving AITP 2016. Obergurgl, Austria.
Kinyon, M. (2015). Automorphic loops and their associated permutation groups. LMS/EPSRC Durham Symposium: Permutation groups and transformation semigroups. University of Durham, UK: LMS/EPSRC Durham Symposium.
Kinyon, M. (2017). Loops and their multiplication groups. All Kinds of Mathematics Reminds Me of You. University of Lisbon: University of Lisbon.
Kinyon, M. (2017). Proof simplification and Prover9. Simplicity of Proofs in Automated Reasoning. Caparica, Portugal: Nova University of Lisbon.
Kinyon, M. (2018). Nonassociative right hoops. Non-commutative Structures . Portoroz, Slovenia: University of Primorska.


  • 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