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.
