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It was Pythagoras
Pythagoras, a Greek mathematician, invented the Pythagorean Theorem, which is that the hypotenuse of a right triangle is the side opposite the right angle. The equation is a2+b2=c2.
Pythagoras was a Greek geometer from Samos. He founded a society of individuals that devoted their lives to mathematics. The Pythagoreans were attributed to him.
algebra isn't a discovery, rather an accumulation of knowledge as we began to process the different kinds of mathematics. Most notable was probably the greek philosopher and mathematician Pythagoras (for which the Pythagorean theorem is names) who extensively studied geometry and how different equations could be used to compute the differences between them. But you should also look to Aristotle, Lucretius, Galileo, etc. Many, many, many men have contributed to the ever-evolving study that is mathematics.
Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof.