Bhāskara II and the Pythagorean Theorem

If I had more time, I would read original treatises in mathematics. The reason is because — when I do get a chance to go over such writings — it is so much clearer to me that math isn’t just a bunch of static pronouncements that everyone agrees about, but a conversation built on emergent logic. Take this manuscript by Bhāskara II (d. 1185), which mathematically proves the Pythagorean Theorem — Bhāskara came to it independently from other scholarship.

Bhāskara II was an ultra-talented scholar from India who wrote a ton of really important stuff on astronomy and engineering, but is most known for his mathematical works, outlining concepts about zero, solving complex indeterminate equations, and giving preliminary concepts about infinitesimal calculus — many of his solutions were only discovered by European mathematicians centuries later.

The formula shown here (this manuscript is from the 17th c) is a “dissection proof” of the famous statement a²+b²=c², which means that you can show it by cutting up the various pieces to demonstrate congruences (see second image).

There are two humanizing aspects of Bhāskara’s writings that I also like. One is that he called one of his mathematical writings _Lilavati_ which means “beauty”, perhaps named after his daughter. This quote about Lilavati shows the congruences among his love for his daughter, for beauty, and for math: “Joy and happiness is indeed ever increasing in this world for those who have Lilavati clasped to their throats, decorated as the members are with neat reduction of fractions, multiplication and involution, pure and perfect as the solutions, and tasteful as is the speech which is exemplified.”.

The second is an apocryphal legend about how Bhāskara proved the Pythagorean Theorem. He was said to have drawn his diagram out and just stating one word: “BEHOLD!”. The idea is that he knew how perfect his diagram was.