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Thursday, January 17, 2019

Maths discoveries by amateurs and distractions by cranks | Opinion & Analysis - The Irish Times

The fact that certain problems are impossible to solve does not deter enthusiasts, writes Peter Lynch, emeritus professor at UCD school of mathematics and statistics, blogs at thatsmaths.com

Srinivasa Ramanujan, one of the most brilliant mathematicians of the last century, wrote unsolicited letters to three leading mathematicians at Cambridge
Photo: The Irish Times 
Do amateurs ever solve outstanding mathematical problems? Professional mathematicians are aware that almost every new idea they have about a mathematical problem has already occurred to others. Any really new idea must have some feature that explains why no one has thought of it before.

It is both difficult and rare to come up with a truly original idea. Such insights almost invariably result from an extended period of intensive work. If one mathematician thinks of something original, why would others not have done the same? Yet, there are those who convince themselves, without justification, that they have done what no one else could do.

Pseudomaths
Pseudomathematics is an activity that fails to observe the rigorous standards of formal mathematical practice and proof. Pseudomathematicians who persist in this activity become cranks. Most professional mathematicians have received communications that contain “proofs” of long-open problems. Often, these claim solutions of problems that have been proven mathematically to be impossible to solve...

The British mathematician and logician Augustus De Morgan wrote a book, A Budget of Paradoxes, in which he introduced the term pseudomath. As an example of a pseudomath, De Morgan mentioned one James Smith who claimed persistently to have proved that pi is equal to three and one eighth. De Morgan wrote that Smith “is beyond doubt the ablest head at unreasoning, and the greatest hand at writing it.”

In the past, many European scientific academies were bombarded by circle-squarers, angle-trisectors and cube-duplicators demanding immediate recognition of their mathematical achievements.

Source: The Irish Times


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