Dr Guerino Mazzola PhD

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Professor: Creativity, Improvisation, and Mathematical Music Theory

Guerino Mazzola earned his Ph.D. in Mathematics from Zurich University, where he also qualified as a professor in algebraic geometry with Peter Gabriel and in computational science with Peter Stucki.

Mazzola has profiled the European school of mathematical music theory since 1980 and has written six books on the subject, among them The Topos of Music, published by Birkhäuser, and proposed  by the American Mathematical Society as the mathematics book of the year 2005. His French book, La vérité du beau dans la musique, is about the philosophy of music and was published in 2007 by Delatour. Mazzola’s approach to music includes sophisticated mathematics of topos theory, but also classical tools from group theory to homotopy theory. His book Flow, Gesture, and Spaces in Free Jazz - Towards a Theory of Collaboration was published in 2009 by Springer and applies mathematical gesture theory to free jazz. His book Musical Performance was published in 2010 by Springer; it is the first comprehensive treatment of performance theory, including philosophical and empirical approaches, qualitative methods from musical ontology, and quantitative methods from differential geometry and their implementation in the performance software rubato. His book Musical Creativity was published in 2011 by Springer; it is co-authored with Joomi Park and Florian Thalmann and describes creativity in a tutorial for students, a theoretical part and a number of advanced case studies. His book Computational Counterpoint Worlds, co-authored with Octavio Agustin and Julien Junod, and his book Computational Musicology in Hindustani Music, co-authored with Soubhik Chakraborty et al.  are published in 2014 by Springer. His new book, The Topos of Music III: Gestures, is published in 2018 by Springer, and co-authored with René Guitart et al., it presents latest developments in musical gesture theory and its philosophical implications. It is a follow-up of The Topos of Music. Co-authored with PhD Students Maria Mannone and Yen Pang, a first introduction to Mathematical Music Theory: Cool Math for Hot Music, is published by Springer Fall 2016. Springer publishes the book Basic Music Technology in 2018. It was written with eight students as co-authors.

Educational Background & Specialties

Educational Background

  • Ph.D.: Mathematics, Zurich University, Zurich, Switzerland.


  • classical symbolic thinking in music and performance theory
  • transformational theory using category theory
  • software for musical analysis, composition, and performance
  • gestures in music
  • free jazz
Research & Professional Activities


  • Swiss National Science Foundation: Research Leader
  • the Hassler Foundation: Research Leader
  • the Cogito Foundation: Research Leader
  • the Art Mentor Foundation: Research Leader
  • the Volkswagen Foundation: Research Leader
  • the Swiss Virtual Campus Initiative: Research Leader
  • IRCAM: Research Member, 1999 - Present
  • Philosophical Laboratory of Charles Alunni at the Ecole Normale Supérieure: Member, 2006 - Present


  • Documentary movie "Brain Concert": consultant, pianist, scientist for documentary movie directed by Bruno Moll on musical creativity and perception and brain research, Spring 1998 - Fall 1998
  • Documentary movie "Teak Leaves at the Temples": Music director, pianist and composer for documentary movie directed by Garin Nugroho on free jazz and Idonesian culture, August 2006 - August 2007
  • CD "Airegin", alyer records: composer, jazz pianist, live recording with quartet, at Airegin club in Yokohama, Japan, October 2004 - October 2004
  • CD "Liquid Bridges": Free Jazz CD recording related to U of M course in Free Jazz, 2008
  • CD "Dancing the Body of Time": Recording at a Live Performance in Tokyo's Jazz Club Pit Inn, 2010
  • CD "Passionate Message": A synthesis of contemporary and free jazz music for two pianos, Spring 2012
  • Summary of opera "Apocalypse Now...and Then", DVD recording: David Walsh and I have written and conceived an opera, with composer Manuela Kerer, about the universe, its musics, God, his wife Ashera, Jesus, and Mephisto. It includes new projecton technologies for stage and sensor systems for dancers, November 2010 - July 2012
  • See my homepage http://www.encyclospace.org/CV/mazzola.html for a complete list of the over 150 papers, 30 books, and 27 CDs/LPs
  • Gruppen und Kategorien in der Musik. Mazzola, Guerino, Heldermann, Author, 1985.
  • Rasterbild - Bildraster, CAD-gestützte Analyse von Raffaels "Schule von Athen". Mazzola, Guerino, Rainer Hofmann, Detlef Krömker (Co-Authors), Springer, Author, 1986.
  • Geometrie der Töne. Mazzola, Guerino, Birkhäuser, Author, 1990.
  • Ansichten eines Hirns - Perspektiven der aktuellen Hirnforschung. Mazzola, Guerino, Ernst Hunziker (Co-Author), Birkhäuser, Author, 1990.
  • Manual for Music Software Presto. Mazzola, Guerino, SToA Music, Author, 1989-1994.
  • Semiotic Aspects of Music. In: Semoitics Handbook, Vol.III: Mazzola, Guerino, Roland Posner et al., de Gruyter, 1999.
  • The Topos of Music. Mazzola, Guerino, Birkhäuser, Author, 2002.
  • Perspectives in Mathematical Music Theory. Mazzola, Guerino, Emilio Lluis Puebla, Thomas Noll (Co-Editors), epOs, Author, 2004.
  • Comprehensive Mathematics for Computer Scientists, Vols. I, II. Mazzola, Guerino, Gérard Milmeister, Jody Weissmann (Co-Authors), Springer, Author, 2004. Link
  • Elemente der Musikinformatik. Mazzola, Guerino, Roland Bärtschi, Stefan Göller (Co-Authors), Birkhäuser, Author, 2006. Link
  • Penser la musique avec les mathématiques?. Mazzola, Guerino, Gérard Assayag, François Nicolas (Co-Authors), Delatour, Author, 2006.
  • La vérité du beau dans la musique. Mazzola, Guerino, Delatour, Author, 2007.
  • Flow, Gesture, and Spaces in Free Jazz- Towards a Theory of Collaboration. Mazzola, Guerino, Paul B.Cherlin, Springer, Author, 2009. LinkImage
  • Musical Performance. Mazzola, Guerino, Springer, Author, 2010. Image
  • Musical Creativity. Mazzola, Guerino, Joomi Park, Florian Thalmann, Springer, Author, 2011. Image
  • Computational Musicology in Hindustani Music. Mazzola, Guerino, Soubhik Chakraborty, Swarima Tewari, Moujhuri Patra, Springer, Author, 2014.
  • Cool Math for Hot Music. Mazzola, Guerino, Y Pang, M. Mannone, Springer, Author, 2016.
  • All About Music. Mazzola, Guerino, M. Mannone, Y. Pang, M. O'Brien, N. Torunsky, Springer, Author, 2016.
  • The Topos of Music, 2nd ed. vol. I-IV. Mazzola, Guerino, R. Guitart, J. Ho, A.Lubet, M. Mannone, M. Rahaim, F. Thalmann, Springer, Author, 2018.
  • Basic Music Technology. Mazzola, Guerino, Y Pang, W Heinze, K Gkoudina, G Afrisando, J Grunklee, Z Chen, T Hu, Y Ma, Springer, Author, 2018.
  • The Future of Music. Mazzola, Guerino, Yan Pang, Jason Noer, Jay Afrisando, Chris Rochester, William Neace, Shuhui Yao, Springer, Author, 2020.
  • Medal of the Mexican Mathematical Society, 2000
  • Reviewer for the Mathematical Reviews, 2001
  • Reviewer for the Zentralblatt für Mathematik, 2002
  • Editorial Board member of the Journal of Mathematics and Music, 2006
  • Membre du Comité scientifique du Laboratoire disiplinaire "Pensée des sciences", Ecole Normale Supérieure, Paris, 2007
  • Editorial Board member of the journal of interdisciplinary music studies, 2007
  • President of the Society for Mathematics and Computation in Music (SMCM), December 31, 2007
  • Editorial Board Member of book series Computational Music Science of Springer, 2008
  • Outstanding Advising & Monitoring Award 2016