The End of Science and Math? The Omega Man: Gregory Chaitin, a mathematical researcher at IBM, has discovered a number, Omega, that is uncomputable and demonstrates that it crops up all over mathematics and blows holes in the consistency of mathematical theory.

Chaitin has shown that there are an infinite number of
mathematical facts but, for the most part, they are unrelated
to each other and impossible to tie together with unifying
theorems. If mathematicians find any connections between
these facts, they do so by luck. “Most of mathematics is true
for no particular reason,” Chaitin says. “Maths is true by
accident.”

This is also bad news, for example, for physics. It implies, he shows, that ‘there can
never be a reliable “theory of everything”, neatly summarising
all the basic features of reality in one set of equations.’ In other words, he claims nothing less than that there are fundamental limits on what we can know. New Scientist
A Google search for <a href=”http://www.google.com/search?num=100?client=googlet&q=Gregory%20Chaitin
“>”Gregory Chaitin” provides further references, the text of some of his technical papers, and a pointer to his home page at IBM.