Michael Kinyon


  • Faculty

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.

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. (2016). 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