From Engineering to Mathematics | Prof. Vishal Vasan on PDEs, Inverse Problems & AI

In this episode of the Know Your Scientist series, we speak with Dr. Vishal Vasan about his journey from mechanical engineering to applied mathematics, his work on partial differential equations, inverse problems, dynamical systems, and his honest views on AI for PDEs. This conversation goes far beyond formulas. Dr. Vasan shares why mathematics is not just a subject, but a deeply human and cultural activity, why most interesting problems are hard, how inverse problems appear in the real world, and what students should really focus on if they want to build a future in mathematics and science. A thoughtful and wide-ranging discussion for students, researchers, and anyone curious about how mathematics connects to physics, data science, AI, climate, and the way we think. Timestamps 00:00 Intro 00:21 Welcome to Know Your Scientist 01:43 From mechanical engineering to applied mathematics 03:47 PhD at the University of Washington 04:51 Why partial differential equations? 06:08 Penn State and the postdoc experience 07:52 How Dr. Vasan sees mathematics 09:18 Mathematics as a human and cultural activity 12:03 Did he ever fear mathematics? 16:09 Why nonlinear PDEs are hard 20:03 PDEs, dynamical systems, and why time matters 21:48 Numerical and analytical tools for solving PDEs 22:39 Fourier theory, Euler, and how applications shape mathematics 29:51 Real-world applications and inverse problems 32:52 Oil exploration, scattering, CERN, and LIGO 35:01 Ocean pressure data and reconstructing wave height 36:36 What makes inverse problems difficult? 40:38 AI and machine learning for PDEs 42:34 Dynamical systems and data science 45:20 Collaboration and connecting ideas across fields 46:36 Skills and habits students should develop 52:06 Future of mathematical sciences in India 54:33 Institutional and cultural changes needed in science 58:33 Life beyond mathematics 59:38 Mentors and influences 63:37 How mathematics shapes the way you think 65:02 Message for students and early-career researchers 67:12 Closing remarks #Mathematics #AppliedMathematics #PDE #InverseProblems #AI #DataScience #DynamicalSystems #DrVishalVasan #KnowYourScientist #Research