Gregory Chaitin

Gregory Chaitin spent a career proving that mathematics is not what mathematicians wished it to be. Where Hilbert had dreamed of a complete and mechanical edifice, Chaitin found at the foundations a number whose digits are random—not unknown, not merely hard, but random in the strict and terrible sense that no theory shorter than the digits themselves can produce them. He called it Omega, the halting probability, and it is the most concentrated piece of irreducible mathematical truth ever exhibited. Chaitin’s deepest insight is also the simplest to state: understanding is compression. To comprehend a phenomenon is to find a description shorter than the phenomenon itself—a law, a theory, a program—from which the phenomenon can be regenerated. Newton did not memorize the positions of the planets; he found equations from which all those positions follow, and the equations are vastly shorter than the data. This is not a metaphor: there is a precise and well-known equivalence between the length of the shortest