The Unreasonable Effectiveness of Mathematics in the Natural Sciences
TL;DR — Wigner’s 1960 essay on why mathematics invented for its own sake keeps turning out to describe physical reality.
Communications in Pure and Applied Mathematics, Vol. 13, No. 1, February 1960.
Wigner’s puzzle: mathematicians develop structures for internal reasons, and those structures then describe the physical world with accuracy far beyond anything that went into them. He calls it “a wonderful gift which we neither understand nor deserve.”
Nine pages, and the question has not been answered. It remains the standard reference point for every argument about mathematical realism, and for the question of whether the effectiveness is a fact about the universe or about how we select which mathematics to notice.
Where this came from
9 pages. A copy is archived locally against link rot; the header links the original source.