The unreasonable effectiveness of mathematics is a phrase introduced by Wigner (1960) for the unexpectedly broad and accurate applicability of mathematical structures to the physical sciences. The issue is not merely that mathematical models can describe observations, but that abstract ideas developed without a particular application in mind often later become precise descriptions of nature. Wigner described this usefulness as an empirical "gift" rather than a consequence that science can take for granted.
The phrase is now used more broadly for the recurring transfer of mathematical ideas between apparently unrelated subjects, although such uses should be distinguished from a mathematical theorem (Big Think 2026).
