[1][2] In it, Wigner observes that a theoretical physics's mathematical structure often points the way to further advances in that theory and to empirical predictions.
He writes: "It is important to point out that the mathematical formulation of the physicist's often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena.
"[3] He adds that the observation "the laws of nature are written in the language of mathematics," properly made by Galileo three hundred years ago, "is now truer than ever before."
Originally used to model freely falling bodies on the surface of the Earth, this law was extended based on what Wigner terms "very scanty observations"[3] to describe the motion of the planets, where it "has proved accurate beyond all reasonable expectations.
Born, Jordan, and Heisenberg then proposed to replace by matrices the position and momentum variables of the equations of classical mechanics.
But Wolfgang Pauli found their work accurately described the hydrogen atom: "This application gave results in agreement with experience."
The equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell's death.
The responses the thesis received include: Mathematician and Turing Award laureate Richard Hamming reflected on and extended Wigner's Unreasonable Effectiveness in 1980, discussing four "partial explanations" for it,[5] and concluding that they were unsatisfactory.
The earliest lifeforms must have contained the seeds of the human ability to create and follow long chains of close reasoning.
[8][15] This theory, referred to as the mathematical universe hypothesis, mirrors ideas previously advanced by Peter Atkins.
Ivor Grattan-Guinness found the effectiveness in question eminently reasonable and explicable in terms of concepts such as analogy, generalization, and metaphor.