MIT Complexity Theorist: Why You Can Do Better Than “Optimal” On Leetcode & SAT | Ryan Williams

Ryan Williams is a professor at MIT and the winner of the Gödel Prize in theoretical computer science. I interviewed him all about his work starting by asking him a popular Leetcode question (3 SUM).

Correction: In this podcast I say "lower bound" when I mean "upper bound" and vice versa. Was speaking using the intuition that lower is better for running time. In reality, the accurate usage is:

"Lower bound" = A proven floor for a problem e.g. "no algorithm can possibly be faster"

"Upper bound" = A proven ceiling for a specific solution e.g. "there exists an algorithm this fast"

Professor Williams answers as if I spoke accurately so the error didn't impact the flow of conversation. Just a correction for the record

• My ergonomic keyboard project I mentioned, you can follow along here: https://read.compose.llc/

• The Kickstarter page for it: https://www.kickstarter.com/projects/ryanlpeterman/compose-simple-ergonomics-beautifully-done

Podcast links:

• YouTube: https://youtu.be/AaK1SL2i_4Y

• Apple: https://podcasts.apple.com/us/podcast/the-peterman-pod/id1777363835

• Transcript: https://www.developing.dev/p/mit-complexity-theorist-on-leetcode

Thank you to this episode's sponsor for supporting my work:

• WorkOS: makes your app Enterprise Ready with easy to use APIs to add SSO, SCIM, RBAC, and more in just a few lines of code, check them out at https://workos.com/

Timestamps:

(00:00) Intro

(00:41) Asking him a popular Leetcode question

(03:54) Doing better than the popular optimal solution

(08:26) Fine grained complexity

(17:00) A severe strengthening of P vs NP

(24:38) SAT problems and solvers

(34:51) Hot takes on famous open questions

(46:57) Simulating space with time

(01:01:02) Why he solves hard problems

(01:02:35) How to pick good research direction

(01:07:14) Technical book recommendations

(01:08:31) Advice for his younger self

(01:11:56) Outro

Where to find Ryan:

• Wikipedia: https://en.wikipedia.org/wiki/Ryan_Williams_(computer_scientist)

• Website: https://people.csail.mit.edu/rrw/

• LinkedIn: https://www.linkedin.com/in/r-ryan-williams-a1b534a/

• X/Twitter: https://twitter.com/rrwilliams

Where to find Ryan:

• Newsletter: https://www.developing.dev/

• X/Twitter: https://x.com/ryanlpeterman

• LinkedIn: https://www.linkedin.com/in/ryanlpeterman/

• Threads: https://www.threads.com/@ryanlpeterman

• Instagram: https://www.instagram.com/ryanlpeterman

• TikTok: https://www.tiktok.com/@ryanlpeterman

Referenced in this episode:

• Some Estimated Likelihoods for Computational Complexity: https://people.csail.mit.edu/rrw/likelihoods.pdf

• Simulating Time with Square-Root Space: https://arxiv.org/abs/2502.17779

• Cook and Mertz's tree evaluation paper: https://dl.acm.org/doi/10.1145/3618260.3649664