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I am someone in the world that you don't know of (my mom says I'm not allowed to expose myself) well here is my answer: Archimedes is the Father of Mathematician and he contributed a lot in mathematics. He gave the basic concepts of Calculus. Moreover, he also gave various other mathematics concepts. Most of the people think that Euclid is the father of mathematics but they are wrong because Euclid is the father of geometry.
Here are 5 interesting mathematicians-P.C. Mahalanobis,S.Ramanujan,aryabhatta,Biswatosh Sengupta,Harish Chandra
He is one of the supervisors of WikiAnswers.com's math section. He is also a mentor and part of the vandal patrol. Mathdoc is a medical doctor and a mathematician as well. He is here to help with all your math questions. Below is a link to his bio page.
If I understand you correctly, you would like us to provide you with a list of mathematicians, no matter their area of concentration, over a two thousand year time period. We're not here to write research papers of that magnitude. If you could narrow your request, you might receive a more satisfying answer.
There are many different methods: the simpler methods will generate lots of triplets but not all. Comprehensive generators tend to be very complex. So here is a simple one: Euclid's formula Take any two positive integers x and y and suppose x > y. Then A = x2 - y2 B = 2xy C = x2 + y2 form a Pythagorean triplet.