Fields Medallist Sir Michael Atiyah recently visited ICTP to share his broad insights on the future of mathematics.

Sir Michael Atiyah

"Until some 20 years ago, modern physics and mathematics seemed to be set on different unrelated paths of discovery. Since then, however, their paths have been crossing with increasing frequency as theories in physics have enriched mathematics and as mathematical concepts have shaped and directed pathbreaking insights in physics."

These were some of the observations made by Sir Michael Atiyah, a Fields Medal winner (1966) and one of the world's most renowned mathematicians, during his recent visit to ICTP. Atiyah travelled to Trieste to participate in the ICTP/SISSA (International School for Advanced Studies) Colloquium on Geometry, which was held in honour of M.S. Narasimhan, long-time head of ICTP's Mathematics group who was celebrating his 70th birthday.
"When the ties between mathematics and physics first began to take hold about two decades ago," Atiyah notes, "it was not clear whether practitioners in these fields would be crossing paths quickly and quietly in the night or forging active long-term ties. Two decades later, the union has proven to be an enduring one--stronger today than ever before." Atiyah's cooperative research efforts with the renowned string theorist Edward Witten, which has led to a recent joint publication, is just one example of this growing relationship between the two disciplines.
Atiyah, formerly a professor at Oxford and Cambridge, UK, is no stranger to efforts seeking to find common intellectual ground between different fields of knowledge. In the 1960s, he and Isadore Singer of the Massachusetts Institute of Technology (MIT), proved the 'index theorems,' a mathematical concept providing powerful connections between geometry, topology, algebra and ultimately quantum field theory. He also developed a branch of geometry called K-theory, which was initially concerned with the interrelationship between topology and linear analysis, but ultimately exerted an important influence on physics, including string theory.
"The things that interest me in mathematics," says Atiyah, "are the interconnection between different parts of mathematics" and the way "in which mathematics can unify and simplify our quest to answer difficult problems, whether in mathematics itself or in other scientific fields."
Atiyah's quest to respond with clarity and precision to difficult questions has not been limited to the classroom and blackboard. Serving as president of the Royal Society (1990-1995) in the UK and the internationally renowned Pugwash community (1997-2002), which has included such luminaries as Albert Einstein, Bertrand Russell, Max Born and Linus Pauling, Atiyah has been a leading voice in discussions related to the role of science in society. While heading the Royal Society, he helped to launch the InterAcademy Panel on International Issues (IAP), an association of national science academies, whose secretariat is now located in Trieste under the administrative umbrella of the Third World Academy of Sciences (TWAS). Twenty years earlier, Atiyah had been elected a founding associate fellow of TWAS itself.
"With all of the threads being weaved between mathematics and other disciplines, ranging from economics to physics, now it is a great time to be a member of the mathematics profession. There are so many new avenues to explore and questions to ask and answer both as an intellectual challenge and for their applications in solving critical issues of importance to our society. Young--and not so young--mathematicians can truly have some fun crossing different borders both within their own fields and the fields of others."
"Mathematics," Atiyah goes on to say, "is a solitary exercise. You sit and you think hard for hours. It gets boring, so a bit of social interaction adds a whole new dimension and makes life so much more interesting and attractive. Some people don't collaborate and work by themselves, but I find interaction one of the more satisfying parts of what I do."

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