Stolen Credit? Transmission Routes and Historical Injustice

How Kerala mathematics may have reached Europe and why credit went elsewhere

Examine the evidence for possible transmission of Kerala mathematics to Europe via Jesuit missionaries and trade routes, and why this history was suppressed.

Three Dates, One Series

In 1671, James Gregory, a Scottish mathematician, was credited with discovering the infinite series for the arctangent. In 1676, Gottfried Leibniz wrote down the same series for arctan(1), giving the famous expansion that yields π divided by four. Three centuries earlier, in roughly 1370, Madhava of Sangamagrama, a Brahmin mathematician working in a small town in Kerala, had already written down both. His verses are preserved in Sankaravariyar's commentary on the Lilavati, in Putumana Somayaji's Karanapaddhati, and in Jyesthadeva's Yuktibhasa, the world's first textbook of calculus, completed around 1530 CE.

The question is not whether Madhava's work came first. It did, by an unambiguous margin. The question is whether Newton and Leibniz invented calculus independently, or whether the foundational ideas reached them through a chain of contact, translation, and transmission that historians of mathematics have until recently chosen not to look at. This lesson is about that question, the evidence on each side, and what an honest history of mathematics would require us to admit.

The Three Tests of Transmission

Historians of science usually ask three questions when investigating possible transmission of an idea from one culture to another. First, was there opportunity? Could one party have reached the other physically, with enough sustained contact for ideas to move? Second, was there motive? Did the receiving party need exactly what the sending party possessed? Third, was there means? Did the receivers have the linguistic, technical, and institutional capacity to translate and absorb the source material?

If all three tests are passed, transmission becomes the simpler explanation than independent rediscovery. Independent discovery of the same complex result by different cultures is possible. It is also rare. When opportunity, motive, and means all line up, a historian who insists on independent discovery is making a stronger claim, not a weaker one.

For the Kerala school and Europe in the period from 1500 to 1700, all three tests are passed.