Thursday, June 4, 2015

HARTOSH SINGH BAL - What the Death of a French Mathematician in 1832 Can Tell us about the IIT Madras Controversy

The most famous duel in the history of mathematics, if not all of science, took place on 30 May 1832. It ended with Evariste Galois, a French mathematician, being shot in the abdomen. He died the very next day at the age of 20. But, by then, he had already done enough to initiate an entire field of mathematics, now termed the Galois Theory, apart from making a substantial contribution to a number of related areas.

It would be a difficult task to describe his work in a few lines, but it is possible to allude to one of its consequences for those familiar with the formula for solving quadratic equations (equations of the form ax^2 + bx + c= 0 where a is not zero) from school algebra. Similar formulas for polynomials—a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient—of degree 3 and 4 (with highest nonzero x^3 and x^4 terms, respectively) were found in the sixteenth century. In 1825, another brilliant mathematician, Niels Henrik Abel, showed that no such formula could be found for polynomial equations of degree 5. Galois’ work, apart from providing a new proof for Abel’s result, can be used to establish whether such a formula exists for polynomials of any degree and to determine it in the event that it does.

The story of Galois’ life and death is romantic enough without the embellishments that have accrued over the years. In one version, Galois stayed up the night before the duel, writing down the details of the theory that would be named after him. Facts don’t seem to bear this out but even attempts to correct this version of events add their own gloss, making Galois’ death no less tragic and the story no less fascinating. The Evariste Galois archive, set up to assemble all his work, provide translations and assemble a factual account of his life, describes the duel that ended Galois’ life in these terms:

The duel and the events leading to it are blurred by time and the fantasies of novelists and what's worse, biographers. …[I]t is highly improbable that the duel was a plot of the royalists to murder him.… Most probably it was Galois himself who incited this interpretation. He wanted … to appear as a victim of the government, (hoping to) enrage the masses to revolt. He dropped remarks pointing in this direction…in his last letters. The most likely reason is: He was weary of life because of his unhappy love affair, his fruitless efforts at gaining recognition for his mathematical work… and he felt (he had ended up in) a blind alley in politics as well. So his duel was like a staged suicide. One thing is clear … he didn't (set) down his mathematical theory the night before the duel.

Galois’ politics may not have been as consequential, but it was certainly as revolutionary as his mathematics. In 1830, Charles X—the last Bourbon king of France—was faced with the possibility of abdication as the liberal party in opposition gained a majority. In response, he carried out a coup and issued a set of directions that suspended the liberty of the press and excluded much of the middle-class from taking part in future elections. He was soon deposed after a popular uprising and a constitutional monarchy was put in place.

Soon after, Galois became involved in the increasing opposition to this monarchy. However, during the successful insurrection of July 1830, while students from the Ecole Polytechnique—a French public institution for higher education and research—played an important role in the uprising, Galois and his fellow students at the Ecole Normale—instituted as a an establishment for higher education outside the framework of the public university system—were locked in by their director and prevented from participating in the revolt. Galois wrote a strong public letter in protest, which led to his expulsion. In 1831, after his dismissal from the Ecole Normale, he was increasingly drawn into the radical politics of the time and arrested. He was released only in 29 April 1832, barely a month before his death.

A more understanding director, aware of the fact that those who brought radical new ideas to mathematics or the sciences could not be constrained to think conventionally about politics, would have acted differently. It would not be unreasonable to assume that such a director may have saved Galois from the despair that led to his death at 20 when he was just beginning his work as a mathematician.

It is against this extreme example that we must set the events that have recently unfolded at the Indian Institute of Technology (IIT) Madras. A handful of students who had formed an Ambedkar Periyar Student Circle—a discussion forum that focused on the ideology and writings of BR Ambedkar and Periyar EV Ramasamy—disseminated material on their campus questioning the thrust of Narendra Modi’s politics. An anonymous complaint is all it took for Smriti Irani’s Human Resource Development (HRD) ministry to ask for a clampdown on the activities of these students, and a director with no apparent self-respect obliged.

There is little reason to suspect that there is a Galois among the students who have been targeted, but we do need to remember that the freedom of ideas is the very basis for creative thought. Our republic has ensured that the IITs supply a steady stream of technicians—engineers and managers—but very few who are truly creative. We must understand that even technological advances are creative acts and do not originate from those who have settled for the work of a technician.

Part of the problem lies in our approach: we value technicians over creative people, and we shy away from the free play of ideas. Under extreme conditions, pure mathematics may be a refuge for people denied a say in political life—as was the case in the Soviet Union, but most of them were only awaiting a chance to flee a society they had no sympathy for. In the case of technology even the possibility of using it as a refuge does not exist; persons who do not value the society they work for are unlikely to make any lasting contributions to its future.

The incident at IIT Madras is an opportunity to correct this approach. If Smriti Irani was actually interested in education and creative outcomes, she would be headed to the IIT campus to tell the students that while she does not agree with their views, she most fervently believes in their right to voice them.