Who Invented the Quadratic Formula?

Solving complicated mathematical problems is done by using complicated formula—like a quadratic equation. Many branches of mathematics and science made major breakthroughs because of it. Thus, many are curious who invented the quadratic formula.

The Babylonians

One of the earliest and progressive civilizations was the Babylonian civilization. They were known to have used quadratic equations in a limited sense. They developed a crude method of doing this, but with a severe lack of formula usage, especially how to manipulate and transpose equations. So the person who invented the quadratic formula could not have come from them.


An Indian national from Brahma-Sphuta-Siddhanta used negative numbers in solving equations in 628 B.C. or in the 7th century. This mathematician, Brahmagupta, is considered to be the first man who invented the quadratic formula as modern people know it today. However, because his work was not known to mathematicians in Europe in the 19th century, some are of the opinion that he was not the first quadratic formula maker.


Bhaskara was another Indian mathematician who dealt with complicated formula with zero-digits. He was acknowledged by mathematicians in Europe in the 12th century, and thus considered by many as the man who invented the quadratic equation. He even incorporated negative roots but cautioned on too much use of the negative value. He said it was inadequate and unacceptable to many.


However, since he came later than Brahmagupta did, not all mathematicians agree that he was the first quadratic formula maker.


The kingdom of Arabia has a candidate in Al-Khwarizm as far as complex mathematical equations are concerned. He also used these formula earlier than Bhaskara did, using it as early as the 11th century. And furthermore, mathematicians in Europe were aware of his works. He could also well have been the one who invented the quadratic equation with European recognition, beating Bhaskara by a century as the first quadratic formula maker.

Tartaglia and Cardano

Niccolo Fontana Tartaglia of Venice was a superb mathematician and teacher. Together with Girolamo Cardano, a doctor and lecturer from Milan, Tartaglia composed and published his solution to the cubic equation, along with his Treatise on Numbers and Measures. This was to substantiate his desire to be appointed artillery consultant in the Spanish Army.

Tartaglia and Cardano were great scientists but could not have been the men who invented the quadratic equations. They merely improved on the earlier works of Brahmagupta and Al-Kwarhizm, and probably even the Babylonians who had started it all long before.