The Hindu mathematicians Baudhāyana certainly discovered the theorem before Pythagoras [1] and Bhāskarāchārya independenly proved the theorem [2] (though the latter seems it was after Pythagoras).
It is also possible to discover mathematical truths without providing a formal proof. Indian mathematician Srinivasa Ramanujan "independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Of his thousands of results, all but a dozen or two have now been proven correct." [3]
The mathematical statement versus rigorous proof was also a cultural difference: "Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades the foundations of mathematics had come into question and the need for mathematically rigorous proofs recognised. Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights." [3]
To the highly-material Western mind, Hindus can be a little weird sometimes: "A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess Namagiri Thayar. He once said, "An equation for me has no meaning unless it expresses a thought of God."" [3]
It is also possible to discover mathematical truths without providing a formal proof. Indian mathematician Srinivasa Ramanujan "independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Of his thousands of results, all but a dozen or two have now been proven correct." [3]
The mathematical statement versus rigorous proof was also a cultural difference: "Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades the foundations of mathematics had come into question and the need for mathematically rigorous proofs recognised. Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights." [3]
To the highly-material Western mind, Hindus can be a little weird sometimes: "A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess Namagiri Thayar. He once said, "An equation for me has no meaning unless it expresses a thought of God."" [3]
[1] https://en.wikipedia.org/wiki/Baudhayana_sutras#Pythagorean_... [2] http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/Hea... [3] https://en.wikipedia.org/wiki/Srinivasa_Ramanujan