[3] He was a member of the Advisory Board of the TUM Institute for Advanced Study (IAS) (2009-2016), Principal Investigator (PI) of the TUM Cluster of Excellence Cognition in Technical Systems (CoTeSys) (2009-2014) and a member of the Editorial Board of the International Journal of Bifurcation and Chaos in Applied Sciences and Engineering (2005-2015).

He gave guest lectures or carried out visiting professorships in Brazil, China, India, Japan, South Korea, US and Russia.

Klaus Mainzer initially published on the concept of a number, the fundamentals of geometry, space, time, symmetry and quantum mechanics.

He became known as a fundamental theorist of complex systems and artificial intelligence (AI), who considers their social consequences in the age of digitization.

With Leon O. Chua of University of California, Berkeley, he pointed out that the non-linearity and instability are insufficient to explain new structures (emergence).

Based on degrees of predictability and constructiveness, he researched the extent to which mathematical proofs - and thus human thinking - can be reduced to algorithms and computers.

In addition to program verification, Mainzer demands technology design that takes social, ecological, ethical and legal aspects into account in the innovation from the outset.