Young Isaac Newton, sitting beneath an apple tree, sees an apple fall. “Aha! I have discovered gravity!” he exclaims.

But maybe it didn’t happen exactly that way. The mathematician Carl Friedrich Gauss “said that Newton told this story to get rid of stupid persons who asked him how he discovered the law of gravitation.” [1]

Maybe it was that Isaac Newton had a “mathematical mind.” Except at the age of 19, when he was in college, Newton was rather weak in the study of geometry and almost changed his major to law. A little bit later, because there was a plague in London, he went back to the family farm and loafed about. It was because he had some leisure time that Isaac Newton idled away the hours pondering mathematical ideas. From this start he discovered not “gravity” exactly, but the laws of gravity which helped explain how the universe worked. [1]

The mathematicians had been thinking for ages that nature boils down to mathematics. Roger Bacon, a 13th Century friar, “believed that the book of nature is written in the language of geometry.” René Descartes, a mathematician born in 1596, had a dream in 1619: “René,” said a voice, “mathematics is the Open Sesame!” [1] “Open Sesame” is a magical phrase that Ali Baba used to open the mouth of a cave which contained buried treasure. For René Descartes, his dream about mathematics and “Open Sesame” helped convince him “that all of nature was a vast geometrical system…” [1]

“To the Renaissance scientist as to the Greek, mathematics was the key to nature’s behavior.” [1]

But then, around 1800, began to arrive the Non-Euclidean geometries. Before that, the axioms of geometry had been regarded as unshakeable truths implanted in our minds. Plato said education was really about remembering what we already knew. Euclidean axioms such as “a point is that which has no part” and “a line is breadthless length” were truths already incorporated into our minds by the universe. They were there, and we just remembered them. Persons such as Carl Friedrich Gauss, Nikolai Lobatchevsky, and János Bolyai, however, began the process which caused some mathematicians to say we ourselves were creating mathematics and its truths were merely our own inventions. [2]

“Is then mathematics a collection of diamonds hidden in the depths of the universe and gradually unearthed one by one or is it a collection of synthetic stones manufactured by man but nevertheless so brilliant that it bedazzles those mathematicians who are already partially blinded by pride in their own creations?” [2]

The above question about absolute mathematical truth vs. creative illusion is exemplified in a movie from 2008, *The Oxford Murders*. Arthur Seldom uses purported Ludwig Wittgenstein arguments to “prove” there is no way of finding a single absolute truth, an irrefutable argument which might help answer the questions of mankind. Seldom represents the new, Non-Euclidean thinking. He is contested, though, by “Martin”, a young graduate student, who says he believes in the number Pi, in the golden section, and the Fibonacci series. “The essence of nature is mathematical,” says Martin, echoing traditional mathematicians. “There is a hidden meaning beneath reality. Things are organized following a model, a scheme, a logical series. Even the tiny snowflake includes a numerical basis in its structure, therefore, if we manage to discover the secret meaning of numbers, we will know the secret meaning of reality.”

You can see from the above how the weary find rest in mathematics, or at least how they used to until the Non-Euclidean geometries came along. The Non-Euclidean geometries are a major cultural event, equal to the arrival of Charles Darwin’s theory of evolution, according to the late mathematician Morris Kline. [2] Ever since these possibly Cthulhu-inspired geometries appeared, there have been increased arguments about truth. (Background: Cthulhu and the Non-Euclidean Geometries, Ersjdamoo’s Blog, March 21, 2015.)

One such furious argument about truth erupted last week in the Memories Pizza Incident. Doing a Google search on “Memories Pizza” will give you tons of results, so there is no need to go into detail about the Indiana pizzeria. Suffice it to say that passions flared on both sides of the argument. But it at least seems both sides agree with traditional mathematics on this one, i.e. that there is in fact some truth to be found and that Arthur Seldom must therefore be wrong about “no way of finding a single absolute truth.”

——- Sources ——-

[1] *Mathematics and the Physical World*, by Morris Kline. Mineola, NY: Dover Publications, 1981. (Originally published 1959.)

[2] *Mathematics for the Nonmathematician*, by Morris Kline. Mineola, NY: Dover Publications, 1985. (Originally published 1967.)