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 number 1729 has an interesting story in mathematics involving the extraordinary Indian mathematician Srinivasa Ramanujan. G. H. Hardy accounts:

“I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. ‘No’, he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways.’”

Ramanujan had a knack for numbers. Growing up in India at the turn of the 20th century, Ramanujan was largely self-taught. Over his short life time (aged 32), he independently developed nearly 4,000 results in mathematics. He kept his results (without proofs) in notebooks that modern mathematicians are still looking into this day. Nearly all of his results have been proven to be true and have driven research in number theory for the past century. Recently, one of Rumanujan’s results, previously unknown to mathematicians, was an important piece to a 2006 publication.

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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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