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The Amateur Mathematician
December 31, 2017
Could the P versus NP problem ever be solved by an amateur mathematician? Quite possibly.
In fact, this is one area of mathematics where the amateur really could stand a strong chance.
If we define "amateur" in this context simply to mean "anyone not receiving a salary or payment for researching computational mathematics" then that includes a lot of people in the world. Most people with Advanced or Degree level qualifications in Mathematics are probably working in other fields such as accountancy, IT or engineering yet may have - or have the ability to gain! - the skills necessary to crack this intriguing problem.
Furthermore, out of all the Millennium Prize Problems in mathematics (see https://en.wikipedia.org/wiki/Millennium_Prize_Problems) the P versus NP problem is the one that lends itself most readily to the amateur mathematician's brain. Other problems such as the Hodge Conjecture are almost impossible to outline in a simple manner and even a cursory skim through the relevant Wikipedia page will probably fail to ignite the passions of the amateur. The P versus NP problem among all the Millenium Prize problems stands out as fascinating, with an alluring "this might just be do-able" siren-call to it.
And remember that some incredible brains in the fields of mathematics and physics were amateurs. Srinivasa Ramanujan (pictured), one of the greatest mathematicians in history started out as a complete amateur and Albert Einstein, while working at the patent office in Bern, was quietly devising the Theory of Relativity as an amateur physicist and mathematician. And if you consider yourself also to be an amateur mathematician, you are in great proud company : Thomas Bayes, George Boole, Nikola Tesla and Ada Lovelace were all arguably amateur mathematicians too.
Ironically, given the seeming difficulty in cracking the problem, the amateur does have a very distinct advantage over the professional. If the professional mathematician were to spend the next 5 years on a full salary trying to solve it and in the end got nowhere, he or she would be out of a job and unable to pay the mortgage. The amateur, on the other hand, can take leisure time to try and solve the problem, safe in the knowledge that even if he or she fails, his/her job will still be safe and all that has been lost is some hours spent in enjoyable mathematical discovery.