Everyone is taught Pythagoras’ theorem at school – that is right-angled triangle, the square of the longest side (the hypotenuse) is the same as the sum of the squares of the other two sides. This can be see expressed by the formula: a2 + b2 = c2

But did ancient philosopher and scientist invented this formula?

According to historical texts this formula was known to the ancient Babylonians and Egyptians at least a thousand years before Pythagoras was born in 507 BC, and one Indian text from a century before Pythagoras contains the first mathematical proof.

Some research suggests that a sage and an architect name Baudhayana actually gave the Pythagoras theorem before Pythagoras was even born.

Who was Baudhayana?

Not much is known about Baudhayana. However, historians attach the date c. 800 BCE (or BC). Not even the exact date of death of this great mathematician is recorded. Some believe that he was not just a mathematician but in fact, he was also a priest and an architect of very high standards.

Baudhayana in particular is the person who contributed three important things towards the advancements of mathematics:

He gave us the theorem that became known as Pythagorean Theorem.

He gave us the method of circling a square.

He also gave us the method of finding the square root of 2.

Baudhayana wrote what is known as Baudhayana Sulbasutra. It is one of the earliest Sulba Sutras written. Now Sulba Sutras are nothing but appendices to famous Vedas and primarily dealt with rules of altar construction. In Baudhayana Sulbasutra, there are several mathematical formulae or results that told how to precisely construct an altar. In essence, Baudhayana Sulbasutra was more like a pocket dictionary, full of formulae and results for quick references. Baudhayana essentially belonged to Yajurveda school and hence, most of his work on mathematics was primarily for ensuring that all sacrificial rituals were performed accurately.

The later Sulba-sutras represent the 'traditional' material along with further related elaboration of Vedic mathematics.

One of the most important contributions by Baudhayana was the theorem that has been credited to Greek mathematician Pythagoras.

What later became known as Pythagorean Theorem has been mentioned as a verse or a shloka in Baudhayana Sulbasutra. Here is the exact shloka followed by English interpretation:

दीर्घचतुरश्रस्याक्ष्णया रज्जु: पार्श्र्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥

or

dīrghachatursrasyākṣaṇayā rajjuḥ pārśvamānī, tiryagmānī, cha yat pṛthagbhūte kurutastadubhayāṅ karoti.

When translated to English, it becomes:

If a rope is stretched along the diagonal’s length, the resulting area will be equal to the sum total of the area of horizontal and vertical sides taken together.



So if Pythagoras himself had come up with a new proof, it would be impossible to be sure that the scientist himself made the breakthrough. For centuries after his death his followers attributed all their new mathematical theories to their erstwhile teacher.

Parallels in philosophy of Pythagoras and Buddha

Left: Bust of Pythagoras of Samos in the Capitoline Museums, Rome. Right: Gautama Buddha. Seated Buddha from Gandhara. British Museum.

Born on the island of Samos in the Dodecanese archipelago, he spent time in both Egypt and Persia studying with priests and philosophers before establishing his own school in the city of Croton on the south-eastern coast of what is now Italy. The school he founded became more of a cult, or at the very least a monastic community. As well as the dedication to mathematics and music (different songs, in different keys, would start and each day), there was a very strict behavioural code. There were no personal possession, the diet was strictly vegetarian, everyone worked on their theories communally, everyone did gymnastics, and all of it was underpinned by the belief that the soul was immortal and would be reincarnated in another form upon death. There are striking parallels in this philosophy with that of Pythagoras’ exact contemporary, Gautama Buddha (about 563-about 480 BC), and some historians think Pythagoras might even have reached India.

Did Pythagoras possess supernatural powers?

As with many cults, secrecy breeds suspicion. This wasn’t helped by his followers claiming that Pythagoras had special powers: he had a thigh made of gold and could be in two places at once. They also claimed he could tell the future, bite snakes to death and that a river once spoke to him.

Pythagoras. Line engraving by Dambrun after Maréchal.

There were a lot of different rumours about eccentric rules within the movement which eventually brought the set into conflict with the local people of Croton and the school was attacked and burned to the ground, killing many of Pythagoras’ pupils. No one knows whether Pythagoras survived the attack, but one account has him escaping to the nearby town of Metapontum, where he starved himself to death.

However, Pythagoras’ influence is still felt today across many disciplines, including mathematics.

featured image: Pythagoras and Musical Proportion on the fresco “The School of Athens”. Raphael Santi, 1509-1511. Vaticano, Stanza della Segnatura, Rome