Rajesh Gopakumar: Stringing together the forces of nature
December 4, 2025 | Bharti Dharapura & Ayoshi Mondal
Rajesh Gopakumar is a Professor of Theoretical Physics and the Director of the International Centre for Theoretical Sciences (ICTS-TIFR), Bangalore, whose research straddles the areas of quantum field theory and string theory. On his recent visit to IMSc, he presented a public lecture, ‘Why Strings?’, tracing the evolution of ideas that developed into string theory. Ayoshi Mondal (Asian College of Journalism) and Bharti Dharapuram caught up with him to talk about his early interests, public outreach, connections between string theory and mathematics, and science policy.
How did you get interested in physics?
I was interested in mathematics in middle school, but I also liked doing simple chemistry experiments. I didn't find school physics very interesting because I wasn't particularly thrilled by pulleys, inclined planes, and things like that. At some point, maybe in class 9 or 10, I learned that matter is made of atoms. I found it fascinating that all of chemistry is ultimately due to atoms, and I learned about quantum mechanics. I wanted to know more about this subject, which explains all the elements in the periodic table.
I tried to read some popular science books. These were the pre-Internet days, and knowledge was scarce, so you scrambled for it by getting hold of good books. There were very cheap Russian books by some very good authors. There weren't that many libraries, but luckily I lived next to the National Library in Kolkata and managed to smuggle myself in. There was also a whole street of second-hand books near the Presidency College. At some point, I think in class 11, I came across The Feynman Lectures, which was very eye-opening.
I was always debating between maths and physics, but at some level, I felt that physics gives you a deeper appreciation of certain areas of mathematics. I chose to study physics for my undergraduate degree because I felt it would be easier for me to be a physicist and enjoy its mathematical beauty, rather than being a mathematician and trying to do physics.
How would you explain string theory to a general audience?
It is not easy, because you want to strike a right balance between being faithful to the subject scientifically, while not being too technical at the same time. The real essence of quantum mechanics is very unintuitive, even for physicists. There, it is really the mathematics that governs your thinking and it is more difficult to convey.
While talking about string theory, I try to come up with examples or borrow metaphors that others have used. If someone has studied a little physics, they may have seen pictures of iron filings around a magnet. They form lines along a force field that one can visualise. When you bundle many of these lines together, they act in a coherent way as a string. Most people would have seen a violin string, and they know that it vibrates in different harmonics. This is one of the basic things you have to understand about string theory: that there are different vibrational modes and they correspond to more and more energetic excitations of the string.
Forces like electricity and magnetism can be thought of as modes of vibrations of these strings. Quite miraculously, the vibrations of similar strings also describe the force of gravity in a single framework. My research tries to put together these very disparate forces, thinking of them in terms of vibrations of strings.
Can you share some examples of how string theory has contributed to other disciplines?
Some of my work has had an impact on a specific area of mathematics called algebraic geometry, which studies the geometry of various complex surfaces. Mathematicians have been studying these surfaces with many tools of their own, and string theory offers a new perspective to learn more about their topology.
Mathematicians like to find things called topological invariants, surfaces that remain unchanged even when you deform them. For example, since all vadas have one hole in them, mathematicians would say that they have the same topology. It is a way of saying that a vada has only one hole, and that it is different from a football, which has no holes in it. These two objects are topologically distinct because you cannot change the shape of one into the other just by squeezing it, without tearing it apart.
There is a mathematical way to assign a number to each of these surfaces. If two surfaces have different numbers, there's no way you can squeeze or deform one into the other. In the case of the vada, this number is 1, which is the number of its holes. Similarly, a football has the number 0, and a pretzel has the number 3. This is the simplest of examples, but mathematicians also like to find ways of categorising more complex surfaces. In some remarkable way, string theory helps in understanding how to categorise them. In some of my early work, I was trying to understand something called gauge-string duality, but it turned out to have parallels with categorising complex surfaces.
String theory has a long history of good back and forth with mathematics, but recently it has also played a role in understanding aspects of strong interactions, quark-gluon plasma, strongly interacting condensed matter systems, high temperature superconductivity, and dark energy and dark matter in cosmology. String theory has played a role in expanding the space of ideas, the space of models and theories that people use.
How has the interaction between string theory and mathematics been possible?
I think physicists and mathematicians have traditionally always talked to each other. There was a bit of a disconnect in the mid-20th century, when there wasn’t as much communication. But in the 1970s, starting from some developments in quantum field theory, these conversations increased, and people realised that physicists were rediscovering some things that mathematicians had already worked out.
For instance, people like CN Yang realised that there is a clear dictionary between some concepts in mathematics and physics. These very insightful people realised that physicists and mathematicians are really talking about the same thing, but speaking in a slightly different language and thinking about it slightly differently. More people started talking and learning each other's vocabulary, and by the time string theory really matured, this conversation was already in place.
One very nice thing that has happened in the field of string theory is that it has invented almost new mathematical ways of thinking. Physicists think about things in a certain way and come to some conclusions based on their physical intuition, which can be very different from approaches that mathematicians have been taking. In fact, one of the leading figures in string theory, Edward Witten, won the Fields Medal in mathematics for his work on understanding the physics of knots.
Ed Witten is, I think, one person who could really bridge the gap between the two sides, and the same can be said for many of his students. This developed a certain culture in which the conversations happened more easily. In fact, that's how Witten arrived at this theory of knots. He was talking to another very famous mathematician, Michael Atiyah, who mentioned recent developments of people trying to understand knots and how to classify them. And soon after, Witten came up with a way to classify knots from a physics point of view.
Conversations are very important, and I think institutions like Matscience and ICTS try to foster these. A lot of creative things happen just over coffee or conversation. Of course, journals and conferences do help, but having people talk to each other more regularly and learn about each other’s problems in an informal, casual way helps.
String theory is often referred to as ‘the theory of everything’. What are some of the promising approaches in validating it?
I don’t like that phrase very much because it carries a lot of hubris. I think people started using it in the 1980s, because they thought that they would immediately be able to answer many questions about putting together all the forces. However, the progress has been slower than they expected. I think string theory is definitely a theory of something, if not everything. And I am satisfied with that.
About validating string theory: There are now very precise instruments trying to measure things related to the early universe. One is the microwave background, the 3 degree Kelvin radiation coming from the early universe, which appears uniform across the sky. But if you look closely using more precise instruments, you will see very small fluctuations, about one part in 100,000. This inhomogeneity comes from quantum fluctuations in the very early universe, which string theory can potentially say something about.
The other thing is related to the large-scale structure of galaxies. To first approximation, again, the universe looks broadly homogeneous. If you go to the very largest scale, where there are these super-clusters of galaxies, the universe is no longer homogeneous. It looks almost like a neuronal system where there are all these clumps and filaments. This clumping is again due to the same quantum fluctuations in the early universe, which one can potentially use to observationally test things in string theory.
Cosmology has become much more precise in making observations in the last 30 years, but I think we need even more precise measurements to do this. But human ingenuity is infinite. We discovered gravitational waves, which Einstein said humans will never be able to measure. However, people came up with very clever ways to measure it, and so I'm hopeful.
What advice do you have for students who are trying to make a choice between the theoretical and applied sciences?
I think they're both important. We need different kinds of people and different ways of thinking in India. People should make a choice according to their temperament and build on their strengths. Some people are naturally very good at coming up with ingenious experiments, like the one measuring gravitational waves. If you are very creative in putting things together, or have creative ideas about how to make measurements, you may have a flair for experiments. Some people may have a flair for mathematics and theory, and they should consider the theoretical sciences.
Many people in India think that theoretical sciences are the only way to do science. This is a structural weakness in our education system, and maybe even in our outreach. We are not cultivating enough people who like to tinker around, make and build things.
What are some of the improvements in science policy that can be introduced in India?
In terms of education, very broadly, one has to cultivate a scientific temper among young children in schools. Science shouldn't be treated as a book with some facts, which you must memorise and repeat. You should be questioning things happening around you. Even a dripping tap in your house can be interesting, and many complex biological phenomena take place in your garden. Students should be observing things, and the spark of curiosity should not be killed by the school system. We also need labs and places where people have opportunities and encouragement to build their talent. There should be good public libraries, which are still the best repositories of knowledge where one can learn fascinating things.
Scientific institutions also need a different policy. Our institutions have become more and more bureaucratized and centralized, and the system is clogged. Even though there are good people in our institutions, they often underperform in the current system. We need to understand why it is happening and reform our institutional and funding structures. People are trying to bring in some changes with the ANRF [Anusandhan National Research Foundation], but we also have to reform institutions so that scientists have the autonomy to do their science, and are valued and trusted by the funding agency and the public. And, of course, scientists need to be accountable, demonstrating that, given the support, many things can be done. You can hold people accountable in multiple ways, but it is currently being done using very blunt-force instruments. Different structures need to be treated differently.
We should have scientifically strong people leading institutions, and they should be given the freedom to carry out their task. We need to undertake scientific reforms because our systems are still like the systems of the 1980s. It [the current disenfranchisement of scientific institutions in many countries around the world] is a chance for India to actually do things differently and to show that we can be world leaders in science and develop breakthroughs. But we have to provide the right environment and empower people who can bring about that change.
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