While mathematics and physics have underlying differences, the disciplines have had the longest union and the most fruitful exchange in the exploration of fundamental laws of nature, David Gross, Nobel laureate and Director, Kavli Institute of Theoretical Physics, Santa Barbara, the U.S., said on Wednesday.
Making a case for stronger collaboration between mathematics and physics in his lecture on ‘Physics and Mathematics at the Frontier' hosted by the Chennai Mathematical Institute, Professor Gross said recent attempts to construct unified theories of matter and gravity, as in the advancement of string theory, had rejuvenated connections between physics and frontier mathematics.
Professor Gross, a 2004 Nobel laureate in Physics, pointed out that though there had been the proposition that mathematics was the natural language of physics since Galileo, the disciplines had developed in different directions in mid-20{+t}{+h} century. It was only about 10 years ago that the situation changed dramatically.However, while theorists such as Paul Dirac promoted a strategy of physicists and mathematicians searching for new ideas in each other's backyards on the proposition that the disciplines shared the same underlying concepts, it is important to remember that there exist differences between mathematics and physics, Professor Gross said. Mathematics has its foundation in generalisation, abstraction and proof while physics had its thought processes rooted in simplification, guesswork and prediction, he said. This difference starts at the level of basic education where mathematics adopts a top-down approach while physics is taught bottom-up starting with classical mechanics, non-relativistic quantum mechanics and then relativistic physics, Professor Gross said.
While it would have been wonderful — as mathematician Yuri Manin suggested — to master both types of thinking “just as we master the use of a right and a left hand,” the possibility is impossible as it had to violate some kind of uncertainty principle, Professor Gross said.
