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The other is "the history of mathematical analysis" which goes back to the times of Archimedes, who was in the same era as Aristotle and Euclid. These to groups or streams were separate for a long time until Newton invented Calculus, which brought Math and logic together.
Somebody who studies mathematical logic and gives his or her own concepts about it is called a logician. Some well known logicians include Boole and Frege. They were trying to give a definite form to what formal deduction really was. Aristotle had already done such a thing but he had done it with language, Boole wanted to do it with only Symbols...
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