Chasing the Conjecture: The 10-Year Journey to Unify Mathematics and Inspire India’s Scientific Future

The article is an interview between Research Matters and Professor Chandrashekhar Khare, FRS, a mathematician and winner of the Infosys Prize (2010), conducted on the occasion of his recent book, Chasing the Conjecture. Khare discusses the decades-long quest that led to his landmark proof of Serre's conjecture, along with the personal, philosophical, and cultural motivations that drive a life dedicated to pure science.

Khare's journey began in Mumbai, where he was drawn to three intellectual interests: math, music, and literature. A decisive moment came when a professional mathematician visited his home and revealed the depths of even the simplest concepts, posing questions that later connected to the Chinese Remainder Theorem. This sparked his inevitable path to number theory, a field he reveres for its 'irresistible charm': simple questions that a high schooler can understand, but whose solutions turn out to be very elaborate. He cites Gauss's declaration that 'number theory is the queen of mathematics' as cementing his dedication. After formative years at the Tata Institute of Fundamental Research(TIFR), which provided essential time and isolation for his mathematical development, much of his work was later done at Cambridge and UCLA. He embarked on the central project of his career: chasing Serre's conjecture, a broad and highly challenging statement by the 20th-century mathematician Jean-Pierre Serre. The process was a decade-long struggle, from 1995 to the breakthrough in 2004, followed by several years of collaborative work with Jean-Pierre Wintenberger to complete the proof. At its core, the conjecture is about identifying a hidden unity: Khare's work demonstrated that two seemingly disparate structures, which he labels 'Galois symmetries' and 'Ramanujan symmetries', 'appear totally different, but actually have the same DNA. They are the same.' This structural unification not only implies a fresh proof of Fermat's Last Theorem but also contributes a crucial fragment to the even vaster Langlands Program.

For Khare, the book Chasing the Conjecture is more than a narrative of this mathematical feat;it is a cultural artefact and a literary memoir. Writing it took almost4-5 years, including a year of editing, to find the right structure that could convey three things: the mathematics, the mathematician, and the process of doing mathematics. His main motivation was philosophical: to show the general public that mathematics is an essential part of the cultural heritage of humankind, standing alongside painting, music, and literature. While people recognise its usefulness, 'planes wouldn't fly, computers wouldn't be possible without the underlying mathematics', they often fail to appreciate it as an intellectual discipline. He acknowledges the subject's 'unearned reputation of being forbidding esoteric,' often compounded by poor school experiences, and sought to write in a language that would 'plunge the reader into the world of mathematical research,' presenting the atmosphere, vulnerability, and sheer dedication required for creative pursuit.

The article's final message is optimistic about India's mathematical future but stresses the need for greater investment and a shift in perception. Khare notes India's 'very rich long history of mathematics,' citing figures like Madhava and Ramanujan, and argues that India is now in a position to push ahead, but this requires nurturing the talent pool. He draws a vivid analogy to cricket, noting that massive investment and resources mobilised talent through initiatives like the IPL, and argues a similar focus is needed in pure sciences. He concludes that basic science, particularly mathematics, is the ultimate long-term investment:'In a sense, you need basic science to make technological advances possible; training the people here brings the greatest strength to the country, and there are long-term dividends.

(Dr. H. S. Sudhira is an urban planning researcher, geoinformatics specialist, sustainability expert, and a member of the Board of the Public Affairs Centre)

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