The Long Journey Ahead

I want one of the Manta Fellows to win the Fields Medal in my lifetime — and most of you to earn a research mathematics position at an R1 institution. No one from Sri Lanka who stayed after A/Ls has done this yet. I truly believe it is possible. Mathematics is an individual sport, like cricket.

India already has an Abel Prize winner who did his PhD at home: S. R. Srinivasa Varadhan received his doctorate from the Indian Statistical Institute in 1963 under C. R. Rao, who arranged for Andrey Kolmogorov to be present at his thesis defence.

The goal: a research position at an R1 institution

These are professional mathematicians — people who get paid to prove new theorems. Here are the stages, starting from admission to a PhD program.

1. Go to a good PhD program and pass qualifying exams.

   Your goal is to prove a theorem. Don’t rule out applied mathematics — there are theorems in applied mathematics, statistics, theoretical physics, even biology. Mathematics is the study of structures: when new structures appear in any area, they must be written properly, and if they don’t yet exist in mathematics, new structures must be built and theorems proved about them.

   Exit → If you fail — typically after two years — you leave with an M.Sc. and can start again at another program. Some instead pursue a PhD simply to climb university ranks at home. These are not the mentors you want if you want to prove a theorem: people who build simple models with basic undergraduate mathematics, who “prove” big theorems with simple methods in non-peer-reviewed journals, or who write essays about mathematics for a Math Ed PhD. Many people won’t notice the difference. You should learn to spot it.
2. Pick an area and an advisor, and solve a problem.

   Work under your advisor for 3–4 years and solve an actual problem.

   Exit → It’s rare to leave without a PhD after passing qualifying exams. Some write a thesis on a problem the advisor solved long ago, or graduate on the “promise” of returning home.
3. Show you can move forward — and get a postdoc.

   If you solve a real problem and show the ability to keep going, your advisor will typically work with colleagues to find you a postdoc position.

   Exit A → Industry. Expect about six months of learning, but there are high-end industries that welcome mathematics PhDs.
   Exit B (old) → Return to Sri Lanka and join a university, often without even publishing the thesis.
   Exit B (new) → Return to Sri Lanka and join the Manta Institute: train the next generation, continue your research, publish, and be paid through research funding — without working under people who have never proved a theorem.
4. Finish the postdoc — sometimes more than one.

   You work under a professor who hired you for your PhD expertise; you learn theirs quickly, adding a new dimension to your own. My PhD was in Harmonic Analysis and my postdoc in Spectral Function Theory. My advisor, Prof. Ciprian Demeter, did his PhD in Ergodic Theory and learned Harmonic Analysis working with C. Thiele and T. Tao at UCLA.

   Exit → I took this path: I burned out at Caltech and left. Building the Manta Institute for future Sri Lankan students following the path I took feels like my call to a second adventure.
5. Get a tenure-track position (Assistant Professor).

   You have six years, evaluated annually. This is the toughest part: you lead your own research with a unique combination of expertise and form a new small sub-area. Prof. Demeter used Harmonic Analysis to solve problems in Restriction Theory with applications to Number Theory — “decoupling.” Some people don’t get tenure after six years.

   Exit → Tenure (Associate Professor) at a lower-ranked university. Prof. Michael Lacey, a giant of Harmonic Analysis, moved from IU to Georgia Tech — and spoke at the ICM the year after proving the boundedness of the bilinear Hilbert transform.
6. Tenure at an R1 university — the goal.

   No one from Sri Lanka who stayed after A/Ls has reached this level. You now have a permanent research position, likely near age 40. These positions exist to carry out very long projects — even 20–30 years — without fear of losing your job. Your salary still depends on grants, which depend on what you publish. A breakthrough at this stage, before 40, brings a Fields Medal.

   Exit → Some relax and stop researching once permanent. Don’t pick them as advisors — choose an energetic Assistant Professor or a Professor with a strong track record.
7. Full Professor.

   Keep working and you become a Professor of Mathematics, running your own research program with students and postdocs.

8. Emeritus Professor.

   Some stay on after retirement, writing monographs and textbooks. There are exceptions: Prof. Ciprian Foias was doing pull-ups and proving theorems in his 80s; Prof. Jean Bourgain was at the front of the most technical parts of analysis his whole career.

Start with the Prep Program