A new mathematical proof might have just solved the P vs NP equivalent for undecidable problems.
April 14, 2026
Original Paper
Turing or Cantor: That is the Question
arXiv · 2604.10418
The Takeaway
The author proposes a measure of undecidability based on probability distributions of input data. If verified, answering the 'U-complete' question negatively would be one of the most significant theoretical shifts in computer science history.
From the abstract
Alan Turing is considered as a founder of current computer science together with Kurt Godel, Alonzo Church and John von Neumann. In this paper multiple new research results are presented. It is demonstrated that there would not be Alan Turing's achievements without earlier seminal contributions by Georg Cantor in the set theory and foundations of mathematics. It is proposed to introduce the measure of undecidability of problems unsolvable by Turing machines based on probability distribution of i