Mathematical Foundations of Artificial Intelligence (MFAI)


The first decade of this century has seen the nascency of the first mathematical theory of general artificial intelligence. This theory of Universal Artificial Intelligence (UAI) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers culminating in book [Hut05], an exciting sound and complete mathematical model for a super intelligent agent (AIXI) has been developed and rigorously analyzed. The model is actually quite elegant and can be defined in a single line:
The AIXI Model in One Line
(k=now, a=action, r=reward, o=observation, U=Universal TM, q=program, m=lifespan, l=length)


The fundamentals of UAI are already laid out, but there are literally hundreds of fundamental theoretical/mathematical open questions [Hut05,Hut09] in this approach that have not yet been answered. The complexity ranges from suitable-for-short-projects to full PhD theses and beyond.


  • excellent math skills, ideally in information theory or probability or statistics
  • creativity in finding and constructing proofs
  • ability to clearly interpret the meaning of mathematical theorems

Background Literature


  • getting acquainted with the most promising mathematical approach to general AI
  • working on interdisciplinary research questions
  • acquire experience in proving theorems
  • advancing your active math skills


information theory; statistics; decision theory; Kolmogorov complexity.

Updated:  1 November 2018/Responsible Officer:  Dean, CECS/Page Contact:  CECS Marketing