A comprehensive history of mathematics, including biographies of several of the great mathematicians from around the world, can be found here. Some highlights are:
- The Greek contribution, probably the most significant in the BCE, and for much of the first millenium CE, pretty much ceased about the sixth century CE., with the commentaries on the works of Archimedes and Apollonius written by Eutocius.
- The recorded contributions of the mathematicians from India, that began with the earliest of the Sulabhasuthras authored by Baudhayana about 800 BCE, ended with Sridhara's Patiganita about 900 CE, a notable exception being Bhaskaracharya's Lilavati in 1140 CE.
- The Arab and Persian contributions, a dense history spanning a couple of centuries, began where the Indians left off and ceased by about 1150 CE, .
- The Chinese contributions are sparse but spread through out the recorded history.
- The modern era, marked with the publication of the Copernican theory in 1543 CE, is dominated by the Europeans. Unless I missed something, the only mention of a mathematician of Indian or Arab origin during this period is that of Ramanujam.
There are two puzzles in this history. Why did the Indian contribution, quite significant and much celebrated by Amartya Sen in his book, The Argumentative Indian, cease abruptly by the end of the first millenium CE? What precipitated the gap in the European contribution between the sixth century CE and 16th century CE?
One theory is that the rise and spread of Islam during this period, from Europe to South Asia and beyond, stifled science and mathematics. Critics of this theory for example, Professor Sen point to the significant contributions from mathematicians of both Arab and Persian origin, that occurred during Islamic domination. Proponents of the theory, however, dismiss it as a myth, contending that such contributions are merely translations of earlier Greek and Indian works. Perhaps, there's an element of truth in both.
I propose an alternative explanation, building on the theory of heterodoxy, which is the central tenet of Sen's book. In his introductory chapter, Sen offers an impressive array of evidence for a tradition of dissent, argumentation, and public debate in the sub-continent. He contends that this tradition of heterodoxy is the most important underpinning for India's significant contributions to science.
Sen's thesis is neither surprising nor novel. From Aryabhata to Stephen Gould, few outstanding scientists could be accused of orthodoxy. Several, including Leonardo Da Vince and Richard Dawkins, were iconoclasts. There is no denying that creativity thrives in an atmosphere that encourages free discussion and exchange of competing ideas and perspectives.
Freedom of expression is necessary, but not sufficient for the advancement of science and arts. Scientists require resources, and without the sponsorship of wealthy institutions and individuals, their creative endeavors cannot be sustained. During much of history, wealth was concentrated in the hands of the kings and emperors. Be it weaponry, navigation, construction, or irrigation, science and technology can help advance the interests of the rulers and the wealthy. Alexander, Chandragupta, and Akbar must have recognized this convergence of interests.
It's quite a different story with religion. Rooted in fear and ignorance, religion is fundamentally antithetical to science, which aims to advance knowledge. When religion and state are distinct, science could advance with support from the state. If religion ruled, directly as in a theocracy, or by proxy through a captive state, science would suffer. The decline of science in India and Europe can be explained by the rise of theocracies in these regions.
An interesting theory along these lines attributes advances in science in the Middle East to the Abbasid Caliphates, who subscribed to a renegade off-shoot of Islam called Mu'tazili .
Mu'tazila belief system was actively promoted by the Islamic Caliphates and was popular amongst the educated and intellectual elites whilst failing to create appeal amongst the uneducated common mass...
the Islamic Golden Age is a time, which was characterized by the development of a rather anti-Islamic Mu'tazila theology, inspired by the rational reasoning and freethinking of the pre-Christianity Greek Rationalism. And those Muslims scholars, who enriched science, mathematics, medicine, philosophy and rational thinking - the defining elements of the Islamic Golden Age, belonged to the un-Islamic Mu'tazila school, unlike contemporary Sunni Islamic scholars, such as al-Bukhari, Abu Daud and Imam Ghazali et al., of the true Islamic school.
Given these facts, it is totally untenable and silly to claim that the golden era of progress and prosperity of Islamic world was ever positively influenced by Islam but instead, it was made possible because true Islamic ideology took the back seat during that era.
Similarly, the flourishing of creative arts under Akbar's rule in India can be attributed to the emperor's rather lackadaisical interest in Islam, his attempt to found a new religion Din-Ilahi, and his commitment to "a secular legal structure" and "religious neutrality of the state" [ibid. p.18]. Sen's subsequent assertion here that Akbar remained a Muslim, and by implication that Islam fosters heterodoxy and therefore science, is self-serving and irrelevant (see my post, Much Ado About Identity, for a discussion on whether Dr. Abdul Kalam, the current President of India is a Muslim or not).
The rise of democracies in Europe and the US during the latter half of the second millennium, often accompanied by the separation of church from the state, led to rapid advances in science and technology. In democracies, particularly in secular democracies, the drive to solve the economic problems and progress takes primacy over religious interests. That democracies are not subservient to religion was underscored by none other J. Scalia of the US Supreme Court. In a speech delivered at the University of Chicago in 2002, he questions the legitimacy of democracy, because it does not have God's sanction:
[the consensus of Western thought] has been upset, I think, by the emergence of democracy. It is easy to see the hand of the Almighty behind rulers whose forebears, in the dim mists of history, were supposedly anointed by God, or who at least obtained their thrones in awful and unpredictable battles whose outcome was determined by the Lord of Hosts, that is, the Lord of Armies. It is much more difficult to see the hand of God—or any higher moral authority—behind the fools and rogues (as the losers would have it) whom we ourselves elect to do our own will.
It is also pertinent to note in this context that the rise of Christian fundamentalism and the weakening of the Establishment Clause of the US Constitution in recent years is a threat to science, as exemplified by the current controversies over the teaching of evolution and stem cell research.
Science progresses by challenging the status quo. Religion thrives by imposing the status quo. As Thomas Jefferson had cautioned,
[If] the nature of... government [were] a subordination of the civil to the ecclesiastical power, I [would] consider it as desperate for long years to come. Their steady habits [will] exclude the advances of information, and they [will] seem exactly where they [have always been]. And there [the] clergy will always keep them if they can. [They] will follow the bark of liberty only by the help of a tow-rope."
--- Thomas Jefferson to Pierrepont Edwards, July 1801.
It's disingenuous, therefore, to claim any religious origin for scientific advancement. Crediting Christianity with Copernican revolution or Islam with Algebra is like crediting the Czar Nicholas II of Russia with the Bolshevik revolution.