- Person
- Eugene Wigner
- Lived
- 1902–1995
- Field
- Theoretical physics
- From
- Hungarian-American
The story
Eugene Wigner spent his career watching mathematics invented for its own sake turn out to describe nature with uncanny precision. Group theory, developed by pure mathematicians, had become in his hands the language of atomic spectra and nuclear physics. In later life his thoughts turned increasingly to philosophical questions about science.
In 1959 he gave the Richard Courant Lecture in Mathematical Sciences at New York University under the title "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". It was published in 1960 in the journal Communications on Pure and Applied Mathematics. Wigner observed that mathematical concepts developed independently of physics, often so that mathematicians could display their ingenuity and sense of formal beauty, nevertheless keep finding precise applications in physics.
He gave striking examples. Newton's law of gravitation, based on very limited observations of falling bodies and the moon, proved accurate for the planets far beyond reasonable expectation. Matrix mechanics, built on rules mathematicians had worked out long before, gave a calculation of the lowest energy level of helium that matched experiment to about one part in ten million. The quantum theory of the Lamb shift agreed with measurement to better than one part in a thousand. Albert Einstein and Alfred North Whitehead had seen the success of mathematics as a mystery, but Wigner's lecture became the classic statement of the problem. He suggested that biology and human cognition may shape physical concepts as we perceive them, but found the happy match between mathematics and physics hard to explain.
The essay became his best-known work outside technical mathematics and physics, and it has provoked responses across many disciplines. In 1980 the computer scientist Richard Hamming examined four partial explanations and found none satisfying. Others have extended the question to molecular biology, data mining, economics and the philosophy of mathematics, and the physicist Max Tegmark has engaged with it in physics.
More than sixty years later, scientists and philosophers still cite Wigner's essay whenever they ask why the abstract patterns of mathematics fit the physical world so well. Its title has become a familiar phrase, borrowed by writers in fields from computer science to economics to frame the same question about their own disciplines.
Why it matters
Wigner's essay remains one of the most widely discussed reflections on why science works, inspiring debate across many disciplines.
About Eugene Wigner
Budapest-born Nobel physicist who brought symmetry and group theory into quantum mechanics, helped launch the Manhattan Project and designed the first plutonium production reactors.
More about Eugene Wigner
- Eugene Wigner brought group theory into quantum physicsEugene Wigner's 1931 book Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra made the mathematics of symmetry usable by a generation of physicists.
- Eugene Wigner introduced the concept of parityIn his 1927 paper On the Conservation Laws of Quantum Mechanics, Eugene Wigner introduced parity, the mirror symmetry of quantum systems, now a basic idea in physics.
- Eugene Wigner's 1932 function links quantum and classicalIn 1932 Eugene Wigner introduced the Wigner function, a way of picturing quantum states in classical-style phase space now used in quantum optics, chemistry and signal processing.
- The Wigner–Seitz cell helps map crystalsWith his student Frederick Seitz, Eugene Wigner gave his name to the Wigner–Seitz cell, a standard way of dividing up a crystal lattice used throughout solid-state physics.
Sources
- Eugene Wigner Wikipedia
- The Unreasonable Effectiveness of Mathematics in the Natural Sciences Wikipedia
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