Building a bridge between past and future scholarship A humble, mustachioed theorist combines mathematics and physics

Matter can be broken down to molecules, atoms, electrons and ultimately to elementary particles. String theory considers these not as particles, but strings. Professor Yuji Tachikawa, who was appointed a professor at age 36, has built a reputation as a researcher in Quantum Field Theory (QFT), which is related to string theory. So what is QFT? While it is obviously difficult for the general public, it’s similarly difficult for professional mathematicians.

“QFT is a theory that has proven effective in many aspects of physics – it describes the Standard Model of elementary particles and plays important roles in condensed matter theory. Quantum mechanics and general relativity are mathematically well-defined, but not QFT. And yet, its theoretical predictions fit well with experimental results, and it has led to many discoveries in mathematics and physics. I find it interesting.”

Said to be a prodigy from a young age, he participated the International Mathematical Olympiad during high school. The story is also told of how he surprised his fellow students by coming up with a better solution than their teacher’s solution. He ended up choosing to study physics after enrolling in the University of Tokyo’s Faculty of Science.

“Unlike mathematics, which calls for rigor from start to finish, I found that theoretical physics allows more leeway and intuition in play, which is why I felt I was better suited to it.”

Since then, the works of this theoretical physicist at bridging mathematics and physics have achieved worldwide recognition, namely through his role in the discovery of “AGT correspondence” and the phenomenon known as “Mathieu Moonshine.” The former of these was named for the initials of its three discoverers (the other two were Alday and Gaiotto), while the latter takes its name from the context of it being a “ridiculous” discovery (hence “moonshine”) about the Mathieu group M₂₄ in abstract algebra. Both discoveries connected different fields in mathematics and physics, and led to the creation of new directions for research.

“With AGT, I was just asked to verify a conjecture two colleagues of mine came up with when I was at Princeton’s Institute for Advanced Study. It happened that I was the only one capable of doing the necessary calculations. For the other, while discussing with my adviser Professor (Tohru) Eguchi and his former student Professor (Hirosi) Ooguri, I happened to open a numerical table in the Encyclopedic Dictionary of Mathematics and found the same sequence of numbers appear in Ooguri's doctoral dissertation from twenty-five years ago. They were both really just a matter of luck – it’s embarrassing for me to call them achievements.”

Despite the humility of the professor with the unassuming moustache, which he has sported for the past ten years, the fact that his achievements have not simply been lucky accidents is attested by him being honored with a series of prestigious awards, including the Hermann Weyl Prize, the Nishinomiya-Yukawa Memorial Prize and the New Horizons in Physics Prize.

“In the future, I’d like to be able to offer meaningful advice to students as a researcher. That’s the way I feel as someone who has already used up half of his total life as a researcher.”

Tachikawa recalls that as a beginning graduate student, he was studying a subject which was then popular but now is completely forgotten. Had he not changed direction at the suggestion of his late advisor Eguchi, he thinks, he would not be where he is today. On his office bookshelf, the thickly bound and musty spines of physics journals that he rescued as they were about to be discarded seemed evocative of the meaning of the university as a space.