Being Called A Corrupter By His Teacher, This Mathematician Only Received Recognition Before Dying In Poverty

Aadhya Khatri - Apr 05, 2019, 1:57 pm IST


Cantor suffered several episodes of depression because of the criticism on his work of infinity

Infinity is one of the most significant parts of the foundation of modern mathematics. It has been circulated for a long time before Georg Cantor’s study of infinite numbers, and infinite sets were known. Unlike our current approach, ancient Greek and then Indian defined infinity as a philosophical concept rather than a formalism.

However, the man who was associated the most with this concept is Cantor. You may think that with such a significant contribution; he must have been deeply respected and praised by his peers. While he should have had that appreciation, Cantor did not precisely live well at his time. When he first introduced his work on infinity, Cantor's fellow mathematicians were enraged, which led to numerous tragedies happening to Cantor.

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Georg Cantor

Georg Cantor was born in 1845 in St. Petersburg, but he and his family migrated to Germany in search of more favorable weather. He was a gifted child and had the opportunity to be under the guidance of some noted mathematicians, like Weierstrass and Kronecker. When he graduated, he became a professor at the University of Halle when he was at a very young age. Apart from infinity, he had other works on number theory, but he is mostly known for the former.

Before he came up with his famous and controversial work, infinity was not accepted as a thing. Many mathematicians at that time opposed the existence of it. A prime example was Gauss. He said that infinity was merely an expression used when people wanted to refer to limits, and there was no such thing as completed infinity in mathematics.

Cantor’s work went against that widespread belief, so he and his infinity research were under severe criticism, even from his former teacher, Leopold Kronecker. He was math department’s head at the University of Berlin, where Cantor wanted to get a job there. However, because of Kronecker’s opinion about his work, he never had the chance he deserved.

Hugo Kronecker 1909 Crop

Hugo Kronecker

Kronecker belonged to the finitism, which opposed the existence of infinity. He expressed his thought on it by claiming that counting numbers were the work of God; everything different than that was the creation of man.

In Kronecker’s opinion, natural numbers existed, they are the base of mathematics, and any other math objects must be able to be derived from that foundation. So Kronecker disagreed with Cantor when he proved that the set of real numbers is larger than that of natural numbers.

The dispute between them went so far that Kronecker called Cantor a “renegade,” a “scientific charlatan,” or a “corrupter of youth.” About the infinity work, he claimed that the theory had no mathematics property and he did not know what governed it, theology or philosophy.

Kronecker’s acts among other criticism from other mathematicians took a heavy toll on Cantor. He was in severe depression and no longer interested in math. Cantor found joy in other subjects; one of them was the question of whether there were other contributors to Shakespeare’s works. He did publish a few pamphlets on that though.

He still loved math and later came back to it. However, none of his works at that time was as transformative as that of infinity. World War I happened and pushed him into poverty. He passed away in 1918, five years after his retirement.

Although he did not live long enough to the day someone gave his work on infinity justice or better, realized how groundbreaking it is. Cantor received the Sylvester medal, awarded by the Royal Society (London).

Cantor’s infinity has laid the foundation for several later developments in mathematics. David Hilbert, one of the most influential and universal mathematicians of the 19th and early 20th centuries, even created an expression called “Cantor Paradise” when he was talking about set theory and cardinal numbers.

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