Trying to solve real-world problems, researchers often discover that the tools they need were developed years, decades or even centuries earlier by mathematicians with no prospect of, or care for, applicability.

Peter Rowlett, “The unplanned impact of mathematics”, Nature 475, 2011, pp. 166-169.

The Unreasonable Effectiveness of Mathematics …


Scholars have often expressed astonishment for how well mathematics works to describe our physical world. In 1960, Eugene Wigner published an article with the title above commenting 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.

Here are some others’ thoughts:

The most incomprehensible thing about the universe is that it is comprehensible.

— Albert Einstein

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.

— Bertrand Russell

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

— Albert Einstein

Our physical world doesn’t have just some mathematical properties, it has only mathematical properties.

— Max Tegmark

Physicists may have fallen prey to a false dichotomy between mathematics and physics. It’s common for theoretical physicists to speak of mathematics providing a quantitative language for describing physical reality… But maybe… math is more than just a description of reality. Maybe math is reality.

— Brian Greene

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Mathematicians have constructed a very large number of different systems of geometry, Euclidean or non-Euclidean, of one, two, three, or any number of dimensions. All these systems are of complete and equal validity. They embody the results of mathematicians’ observations of their reality, a reality far more intense and far more rigid than the dubious and elusive reality of physics. The old-fashioned geometry of Euclid, the entertaining seven-point geometry of Veblen, the space-times of Minkowski and Einstein, are all absolutely and equally real.

G. H. Hardy

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