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