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| 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.
