In his book Everything and More: A Compact History of Infinity, David Foster Wallace refers to Gödel as “modern math’s absolute Prince of Darkness” (p. 275) and states that because of him “pure math’s been in mid-air for the last 70 years” (p. 284). In other words, according to Wallace, since Gödel published his famous paper in 1931, mathematics has been suspended hanging in mid-air without anything like a proper foundation.

It is high time these dark thoughts were permanently laid to rest. Hilbert’s century-old vision of a static completely mechanical absolutely rigorous formal mathematics was a misguided attempt intended to demonstrate the absolute certainty of mathematical reasoning. It is time for us to recover from this disease!

Gödel’s 1931 work on incompleteness, Turing’s 1936 work on uncomputability, and my own work on the role of information, randomness and complexity have shown increasingly emphatically that the role that Hilbert envisioned for formalism in mathematics is best served by computer programming languages, which are in fact formalisms that can be mechanically interpreted—but they are formalisms for computing and calculating, not for reasoning, not for proving theorems, and most emphatically not for inventing new mathematical concepts nor for making new mathematical discoveries.

In my opinion, the view that math provides absolute certainty and is static and perfect while physics is tentative and constantly evolving is a false dichotomy. Math is actually not that different from physics. Both are attempts of the human mind to organize, to make sense of, human experience; in the cas...