Mathematicians in Kerala, southern India, discovered infinite series well before their counterparts in Europe did, George Gheverghese Joseph of the University of Manchester has argued. This knowledge may even have traveled from India to Europe via Jesuit scholars, influencing European mathematics.
On Sept. 23, at the MAA's Carriage House Conference Center, Joseph spoke about "The Politics of Writing Histories of Non-Western Mathematics." In a provocative address, he cited the example of the discovery of infinite series as one instance in which possible Indian and other Asian influences on European mathematics have been neglected in the past.
"Why are Non-Western contributions generally neglected in histories of science?" Joseph asked. "Why is there such difficulty for new evidence on Non-Western contributions to become accepted and then percolate into standard histories of science?"
To answer these questions, Joseph focused on the nature of the evidence used to establish priority in mathematical discovery and the transmission of mathematical knowledge from one part of the world to another. He contended that the standard of evidence required to establish transmission from East to West was generally much higher than that required for transmission in the opposite direction.
The result, Joseph said, is that European sources generally fail to mention or acknowledge transmission or borrowing of any kind, even when the "circumstantial evidence" may be compelling. He described it as the "problem of invisibility" for non-European mathematics. Western historians and writers need to recognize that they have imposed too broad a burden of proof on the East's importance to the historical development of mathematics, Joseph said.
Westerners often overlook circumstantial evidence and subtler signs of where and how mathematical knowledge has arisen, Joseph noted. In particular cases, Western scholars have also missed another factor in the puzzle of mathematical development: the role of 16th-century Jesuits. These world travelers may well have been the agents who transmitted Chinese and Indian mathematical knowledge to European mathematicians and centers of scientific learning.
As one example, Joseph cited recent research (still in progress) demonstrating that a Chinese mathematician, Zhu Zaiyu (1536–1611), discovered a mathematical method involving the twelfth root of 2 to create an equal-tempered 12-tone musical scale (dividing an octave into twelve equal semitones) no later than 1581. Simon Stevin (1548–1620), who is often credited with the discovery, provided hints of his method only as early as 1585. Marin Mersenne (1588–1648) wrote about equal temperament in his 1637 book Harmonie universelle, possibly after seeing Stevin's work.
But establishing priority isn't enough, Joseph said. "Could this knowledge have been transmitted from China to the West?" he asked.
Joseph and a colleague are now searching for evidence suggesting that transmission of the necessary knowledge could have occurred via the Jesuits in a chain from Zhu Zaiyu to Jesuit scholar Matteo Ricci (1552–1610), who worked in China, to Jesuit mathematician Christopher Clavius (1538–1612) to Niklaas Trigault (1577–1628) to Stevin and Mersenne.
In the case study involving infinite series, Joseph said, the documentary evidence supporting possible transmission to Europe of Indian knowledge is more compelling.
Joseph acknowledged that the situation has improved in recent decades. He noted positive changes in how Europeans and Americans, particularly writers of general math history texts, perceive non-European mathematics. Joseph's own book, The Crest of the Peacock, has contributed to this trend, and he is now working on a third edition.
An Interview with George Gheverghese Joseph
George Gheverghese Joseph's Abstract and Bio
George Gheverghese Joseph's Presentation (audio)