Lex Fridman PodcastPo-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183
CHAPTERS
- 0:00 – 5:17
Awe of engineering: turbulence, elevators, skyscrapers, and bridges
Lex and Po-Shen start with the feeling of wonder that complex engineered systems (airplanes, elevators, tall buildings, bridges) work reliably. The conversation frames civilization as layered abstractions and interdependent networks of expertise.
- •Flying feels miraculous, especially during turbulence
- •Elevators and skyscrapers as everyday engineering wonders
- •Bridges as a visual example of structural elegance
- •Human progress built on networks of specialized knowledge
- •Abstraction layers as the engine of modern technology
- 5:17 – 7:45
Building MS-DOS games from scratch (pixels, fonts, Pascal → C++)
Po-Shen describes writing the Alien Attack games in high school and why the challenge appealed to him. He explains how low-level the tooling was: even drawing letters required manual pixel operations.
- •Motivation: prove you can execute an idea end-to-end
- •Late-’90s era made it feasible for a student to build a full game
- •Graphics primitives were extremely low-level (draw-a-pixel)
- •Fonts/letters implemented via pixel-by-pixel rendering
- •Language progression: Pascal for the first, then C++
- 7:45 – 11:29
Programming competitions and the mindset of efficient algorithms
They discuss what programming contests train: rapid reasoning, simplicity, and algorithmic efficiency. Po-Shen connects contest thinking to real-world scalability constraints in software systems.
- •Computers are powerful; the bottleneck is specifying the right algorithm
- •Contests emphasize writing efficient functions, not full products
- •Human speed matters, but clean solutions matter more than typing speed
- •Algorithmic thinking transfers to startups and large-scale systems
- •Back-of-the-envelope complexity estimates prevent unscalable designs
- 11:29 – 16:47
Why math feels hard: invention vs memorization (and an improv-style classroom)
Po-Shen argues that math should be ‘rewardingly hard’ because it develops invention, not recall. He outlines a teaching approach where students generate ideas first and the instructor “yes-and” guides them toward proofs.
- •Hardness should be about inventing, not remembering procedures
- •Present problems before methods to build the invention muscle
- •Contrasts with “watch me, then repeat 20 times” pedagogy
- •In-person teaching as improvisation: students co-create proofs
- •Online teaching can simulate invention via timed hints
- 16:47 – 29:01
NOVID’s core idea: measuring disease proximity by network distance
Po-Shen introduces NOVID: reframing contact tracing around incentives and predictive information. Instead of only notifying after exposure, the app tells you how many relationship-hops you are from verified illness—encouraging voluntary, self-protective behavior.
- •Classic contact tracing fights incentives (removing people ‘against their will’)
- •Mechanism design/game theory: align selfish behavior with public good
- •Key reframe: proximity is “number of close interactions away,” not meters
- •Stronger incentive when diseases are deadlier (better feedback loop)
- •Goal shifts from past-looking ‘damage control’ to future-looking prediction
- 29:01 – 44:16
Privacy-preserving tech: Bluetooth graphs, sparsity, and scalable computation
They dig into how NOVID can work without GPS by using Bluetooth proximity to construct an interaction network. Po-Shen explains battery constraints, estimating duration via periodic scans, why sparsity makes the graph tractable, and how adoption can become viral.
- •Bluetooth proximity builds a network without revealing location
- •Duration inferred via periodic “snapshots,” relying on statistics
- •Focus on strong, repeated interactions; brief stranger contacts wash out
- •Networks are sparse: the ‘top ~100 interactions’ carry most signal
- •Scalability via near-linear algorithms and hourly recomputation budgets
- 44:16 – 51:49
Adoption, verification, and real-world rollout with public health partners
Po-Shen explains why many contact-tracing apps failed to spread: they benefit others more than the installer. NOVID aims to benefit the user directly, but still needs verified positives and collaboration with local health authorities to prevent abuse.
- •Standard apps notify after exposure—little self-benefit to install
- •NOVID’s value proposition: help you avoid getting sick (if you choose)
- •Verification via expiring passcodes from health authorities
- •Unverified self-reporting exists but is treated differently
- •Big challenge is rollout/adoption; app-building is only part of success
- 51:49 – 54:15
What makes math beautiful: reframing that turns complexity into clarity
After the pandemic discussion, they return to pure mathematics and the aesthetics of problem solving. Po-Shen ties mathematical beauty to perspective shifts that crystallize messy problems into solvable forms.
- •Beauty as the moment a new viewpoint makes a solution visible
- •Reframing is a transferable skill (math ↔ real-world systems)
- •Networks/graphs as a unifying language for many domains
- •Problem-solving as searching a space of representations
- •Mathematics as a tool for simplifying without losing truth
- 54:15 – 1:09:49
International Math Olympiad: format, scoring, and the human side of grading
Po-Shen describes the IMO structure (two days, proof-based problems) and why solving even one problem is exceptional. He also explains partial credit and the negotiation-like grading process across languages and delegations.
- •Most prestigious pre-college math competition; proof/essay solutions
- •Two 4.5-hour sessions, three problems per day; 6 problems total
- •Each problem worth 7 points; max score is 42
- •Partial credit rewards meaningful progress toward a proof
- •Cross-language grading requires coach explanations and careful rubrics
- 1:09:49 – 1:17:36
Hard problems and ‘leaps of insight’: how to read proofs and learn deeply
They explore what makes problems difficult: multiple non-obvious insights with branching search paths. Po-Shen shares how he learned from textbooks by attempting to re-prove theorems before reading the proof, using proof length as a proxy for insight count.
- •Difficulty scales with the number of required perspective shifts
- •Search branching makes 3 insights far harder than 1 insight
- •Textbook reading method: attempt proof before reading it
- •Proof length (within a style/context) roughly signals insight count
- •Research persistence: insights feel good, but many paths are dead ends
- 1:17:36 – 1:28:52
Discovered vs invented math, intelligence as heuristic search, and live problem-solving
Po-Shen argues mathematics is largely discovered and imagines overlap with alien math (e.g., circles and π). They then connect intelligence to heuristics that prune huge search spaces, and Po-Shen describes live-streaming first-time problem solving to expose thinking processes.
- •Math as discovered: simple statements can hide deep necessity
- •Alien communication: math seems universal but still needs alignment
- •Intelligence: heuristic evaluation that avoids brute-force search
- •Heuristics are hard to verbalize (chess-player analogy)
- •Live-solving on YouTube shows real-time invention and error recovery
- 1:28:52 – 1:41:58
Math education in practice: middle school ‘spark’, competitions, and daily habits
Po-Shen emphasizes middle school as the moment math becomes rich enough for genuine discovery. He recommends contest problems and structured hint systems (Daily Challenge) to build invention, and suggests teaching others as a way to learn.
- •Middle school: enough tools (fractions/area) for ‘ancient-math’ wonder
- •Goal: help every student feel capable of inventing, not mimicking
- •Resources: MathCounts, AMC 8/10/12, MathLeague for practice sets
- •Daily Challenge format: timed hints → attempt → multiple solution paths
- •Daily math habit can be practical via teaching/learning with kids
- 1:41:58 – 1:55:27
Combinatorics and voting trees: designing tournaments that pick strong winners
They transition into combinatorics as the study of discrete structures like graphs. Po-Shen explains voting trees as tournament ‘circuits’ and discusses guarantees on how many opponents the winner must beat, including improvements over standard balanced brackets.
- •Combinatorics focuses on discrete, iterative, algorithmic reasoning
- •Voting trees model multi-candidate elections via head-to-head comparisons
- •Balanced bracket can produce weak winners (only beat log₂N opponents)
- •Goal: guarantee winner beats many candidates under any preference tournament
- •Their work improves guarantees to about √N (vs log-scale) using new widgets
- 1:55:27 – 2:05:09
Stochastic coalescence: distributed aggregation, lump sizes, and a small tweak that fixes bottlenecks
Po-Shen describes stochastic coalescence through a ‘sum of sleep hours’ analogy: how to aggregate information quickly without centralized coordination. The analysis shows why large ‘lumps’ can cause √N bottlenecks and how choosing the smallest incoming lump can restore fast convergence.
- •Parallel aggregation can be logarithmic if a perfect tree is pre-assigned
- •Real challenge: forming the tree without linear-time coordination
- •Randomized delegation creates ‘lumps’ whose sizes bias future interactions
- •Risk: one giant lump slowly absorbs many singletons (√N slowdown)
- •Fix: accept the smallest incoming lump to balance sizes and speed up
- 2:05:09 – 2:20:15
P vs NP, campaigns (Tolkien/WWII), advice for youth, and a legacy-based meaning of life
In the closing stretch, they touch on P vs NP and the humility required around deep unknowns. Po-Shen shares inspiration from long ‘campaign’ narratives (fiction and WWII history), then offers life advice centered on invention and ambitious problems, ending with a personal notion of meaning as long-term impact measured in ‘person-years.’
- •P vs NP: Po-Shen declines to speculate deeply; highlights limits of expertise
- •Motivation from ‘campaign’ stories: enduring adversity toward a goal
- •Advice: learn to invent (not just mimic) and aim for important hard problems
- •Regret-minimization: better to try and fail than not try
- •Meaning/joy: maximize long-run impact—ideas that outlast one’s lifetime
