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Mehtaab Sawhney, a Clay Research Fellow and professor at Columbia University has solved one of prime numbers’ many mysteries this fall. Sawhney, who joined Columbia last year, enjoys the thorny work of proving a seemingly straightforward statement of fact. His research interests are broadly within combinatorics, probability, analytic number theory and theoretical computer science.
Prime numbers, which can only be divided by themselves and one, seems to be randomly distributed, but, in aggregate, they actually show patterns that Professor Sawhney unraveled.
Professor Mehtaab Sawhney worked with Professor Ben Green of Oxford University to prove that there are an infinite number of prime solutions to p2 + 4q2, where both p and q must also be prime. It’s one of more than 50 math proofs that Sawhney has solved since starting graduate school, which he completed in a very-speedy-for-a-PhD four years. The findings have been described as “phenomenally impressive” and “terrific” by mathematicians not involved in the research.
For example, 41 is a prime number, and one can write it as five squared plus four times two squared (52 + 4[22] = 41).
There’s actually quite a lot of these at these lower levels, but they get gradually sparser as you get into higher numbers.
Professor Sawhney majored in math and minored in computer science and chose to be in academia for the freedom it offers in day-to-day work, especially with your thinking time.
Talking about Columbia University, Professor Sawhney said, “I grew up on Long Island. I actually came to Columbia in high school for a science honors research program that took place on Saturdays, where we took classes taught by graduate students or postdocs. I’ve always really liked the campus, and the math department has great and collegial researchers. I did my undergraduate and PhD at MIT and a master’s at Cambridge, but I knew I wanted to come back here.”
Professor Sawhney’s educational history includes MIT (September 2020 – June 2024) Doctor of Philosophy in Mathematics; MIT (September 2017 – February 2020) Bachelor of Science in Mathematics with Minor in Computer Science.
