Key Moments
Po-Shen Loh: Mathematics, Math Olympiad, Combinatorics & Contact Tracing | Lex Fridman Podcast #183
Lex FridmanKey Moments
Po-Shen Loh discusses math, innovation, and his app Novid for anonymous contact tracing.
Key Insights
Mathematical concepts like network theory and combinatorics can be applied to real-world problems such as disease control.
The Novid app uses Bluetooth and network theory to provide anonymous contact tracing, focusing on user privacy and empowering individuals to make informed decisions.
Inventing solutions and developing the ability to 'invent' is a crucial skill, applicable in mathematics and beyond.
Programming competitions and math Olympiads foster problem-solving skills, efficiency, and creative thinking, transferable to entrepreneurship and research.
Education should focus on teaching students how to invent and think critically, rather than just memorizing methods.
The beauty of mathematics lies in finding novel perspectives to simplify complex problems and the potential for discovered truths to be universal.
THE BEAUTY OF HUMAN ACHIEVEMENT AND MATHEMATICAL ABSTRACTION
The conversation opens with ponderings on the marvel of human achievements like flight and skyscrapers, highlighting our reliance on a complex network of specialized knowledge. This leads to the concept of abstractions, from basic computer bits to sophisticated AI, underscoring how complex systems are built layer by layer. Mathematical thinking is presented as a fundamental tool that enables these advancements, allowing us to break down and understand intricate problems.
FROM GAMING TO ALGORITHMS: PROGRAMMING AND COMPETITIVE MATH
Loh recounts his early experiences programming games from scratch using Pascal and C++, emphasizing the desire to build complete, functional systems. This transitioned into competitive programming, which, unlike game development, focused on writing highly efficient functions. These competitions taught the value of quick thinking, elegant solutions, and the power of computers to perform tasks much faster than humans, skills he believes are crucial for building startups and tackling large-scale problems.
EMBRACING THE 'HARDNESS' OF MATHEMATICS AS A REWARDING CHALLENGE
Addressing the common perception of math as 'hard,' Loh reframes it not as a memory challenge, but as an 'invention' challenge. He advocates for teaching methods that empower students to discover solutions independently, fostering a sense of accomplishment. This contrasts with rote memorization and practice, emphasizing that the ability to invent and solve novel problems is the true reward and a fundamental skill for lifelong learning and innovation.
NOVid: ANONYMOUS CONTACT TRACING THROUGH NETWORK THEORY
Loh details the creation of Novid, an app developed to combat COVID-19 using network theory and smartphones. Unlike traditional contact tracing, Novid prioritizes user anonymity and emphasizes privacy. It quantifies proximity not by physical distance, but by the number of relationships separating an individual from a potential illness. This approach aims to create positive feedback loops, incentivizing users to protect themselves by avoiding sick individuals, thereby enhancing disease control.
GAME THEORY AND MECHANISM DESIGN FOR DISEASE CONTROL
The underlying principle of Novid is rooted in game theory and mechanism design, drawing parallels to free-market economies over central planning. By aligning individual incentives with the collective good, the app encourages adoption and participation. Loh highlights that the more deadly a disease, the stronger the incentive to use the app, creating an effective feedback loop that empowers individuals to manage their risk anonymously and without coercion, a stark contrast to more authoritarian public health measures.
THE INTERNATIONAL MATH OLYMPIAD AND DEVELOPING 'INVENTORS'
As coach of the USA International Math Olympiad team, Loh emphasizes developing students' capacity for invention rather than just winning. He views the Olympiad as a platform for nurturing critical thinkers who can tackle complex problems, viewing success not just by competition results, but by their future impact. This philosophy extends to his teaching at Carnegie Mellon, where exams are designed to test invention and problem-solving skills on novel material.
THE POWER OF PERSPECTIVE AND THE BEAUTY OF DISCRETE MATH
Loh finds beauty in mathematics through reframing complex problems from different angles, simplifying them. Combinatorics, or the study of discrete structures, particularly appeals to him due to its contrast with continuous mathematics like calculus. He highlights how concepts like network theory, originating from discrete math, can have profound practical applications, from disease spread to voting systems.
COMPLEXITY, VOTING TREES, AND DISTRIBUTED ALGORITHMS
The discussion delves into computational complexity, highlighting its importance in practical applications like disease control. Loh explains voting trees and the challenge of designing efficient circuits for elections, noting that even simple-looking problems can have complex solutions. He also touches upon stochastic coalescence, discussing how distributed algorithms, while seemingly complex, can be optimized from near-logarithmic to near-square root time complexity with clever design choices.
FOSTERING INVENTION AND LIFELONG LEARNING
Loh stresses the importance of developing the skill of invention in individuals, encouraging them to aim for challenging, impactful pursuits rather than settling for comfort. He advocates for a lifelong learning approach, characterized by continuous self-improvement and the practice of thinking critically. Teaching others, even children, is presented as a powerful way to solidify one's own understanding and foster invention.
THE MEANING OF LIFE AND THE LEGACY OF IDEAS
Loh shares his personal philosophy on life's meaning: maximizing the positive impact of one's work that outlasts their existence. He likens this to scientists who continue to influence generations and emphasizes that the ideas we carry and invent are more significant than fleeting individual accomplishments. This perspective fuels his drive to tackle difficult problems with the hope of contributing lasting knowledge and potentially influencing future civilizations or even artificial intelligence.
Mentioned in This Episode
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Learning & Teaching Mathematics: Po-Shen Loh's Approach
Practical takeaways from this episode
Do This
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Common Questions
Po-Shen Loh teaches by presenting interesting questions that students don't immediately know how to solve. He encourages them to 'improvise' and collaborate to invent proofs and solutions. His unique exam format involves open notes but entirely new problems not covered in class, forcing students to invent solutions.
Topics
Mentioned in this video
The national team Po-Shen Loh coaches, which participates in the most prestigious math competition for pre-college students worldwide.
Where Po-Shen Loh worked on stochastic coalescence, showing the practical motivation for theoretical computer science problems.
Academic institution where Po-Shen Loh is a professor and teaches his classes.
An app founded by Po-Shen Loh that uses a novel approach to anonymous contact tracing and provides statistical information about COVID-19 cases in a user's physical network.
A YouTube channel by Grant Sanderson, known for its beautiful and inspiring math videos, but not intended for daily practice.
A flashcard app that Lex Fridman uses daily to memorize things and build his 'thinking muscle' by focusing on new ideas.
Tech company known for its iOS operating system, which Novid had to work around to run efficiently in the background.
A smart mattress company mentioned as a sponsor of the Lex Fridman Podcast.
A social network mentioned as an analogy for 'six degrees of separation' in network theory.
Car manufacturer founded by Elon Musk, used as an example of a company making both software (autopilot) and hardware (cars).
Tech company also attempting contact tracing solutions, against which Novid's approach is implicitly compared for user incentives.
Platform where Po-Shen Loh live-solves math problems and hosts his Carnegie Mellon classes, and where Lex Fridman releases videos.
An online education platform for basic math and science, founded by Po-Shen Loh.
A mental health service mentioned as a sponsor of the Lex Fridman Podcast.
An electrolyte drink mix brand mentioned as a sponsor of the Lex Fridman Podcast.
Po-Shen Loh's PhD advisor, who inspired him to choose problems that 'might matter if you succeed,' influencing his decision to work on Novid.
A famous researcher at Stanford and a friend of Po-Shen Loh, who asks what new tools are learned from solving a math problem, beyond the solution itself.
Chess grandmaster, used as an example to illustrate that even experts have difficulty articulating the full heuristic function behind their intuitive decision-making.
A computer scientist who, humorously, estimates the probability of P ≠ NP at 3%, which Po-Shen Loh finds motivating for researchers.
Creator of the '3Blue1Brown' YouTube channel, whose math videos are seen as inspirational tools but not a daily ritual for math practice.
Collaborator with Po-Shen Loh on a proof demonstrating the behavior of lumps in stochastic coalescence.
From Google, designed IQ-like tests for AI that humans find simple but AIs find difficult, emphasizing AI's current limitations in pattern invention.
Physicist and mathematician, mentioned for his discoveries and his quote about calculating heavenly bodies but not the madness of people.
Mathematician known for proving Fermat's Last Theorem, whose multi-year dedication illustrates the patience required for deep mathematical problems.
Mentioned for his involvement in developing an alien language for the movie 'Arrival', highlighting the challenges of interspecies mathematical communication.
Author of 'The Hitchhiker's Guide to the Galaxy', implicitly referenced via the number 42, which influenced Elon Musk.
Mentioned as an impressive figure in manufacturing, contrasting software-only startups with those building physical products like cars and rockets.
Professor of Mathematics at Carnegie Mellon University, national coach of the USA International Math Olympiad team, and founder of Expi and Novid.
Mentioned by Po-Shen Loh for his ability to make 'obvious observations' that led to profound discoveries, paralleling Novid's simple core idea.
A famous mathematical theorem, used as an example of a simple statement with an incredibly difficult proof that required profound insights.
A major unsolved problem in theoretical computer science concerning whether every problem whose solution can be quickly verified can also be quickly solved.
A simpler way to solve quadratic equations discovered by Po-Shen Loh, which he believes could make it into textbooks and contribute significantly to his 'person-years' impact score.
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