Loh, Po-Shen
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Loh describes his path into competitive programming and mathematics as driven by a fascination with hard, seemingly-impossible problems that are nonetheless learnable — contrasting math olympiad problems (which require inventing a proof, not computing an answer) with the mimicry-based way math is often taught ("watch me do this, now practice it 20 times"). His core teaching philosophy, applied both in his Carnegie Mellon combinatorics courses (exams are 90% of the grade, open-notes, but guaranteed to contain no problem type seen before) and in his free "Daily Challenge" and YouTube live-solving videos, is to give students unfamiliar problems and structured hints so they practice the actual skill of invention rather than memorized methods — arguing this is a generalizable skill relevant far beyond math itself.
He gives an extended account of NOVID, the COVID-19 contact-tracing app he built with a team beginning in March 2020, framing its core innovation as a reframing of the disease-control problem: rather than helping others avoid a sick person after the fact (which gives an individual near-zero incentive to install the app, since it doesn't protect the installer), NOVID tells each user how many "hops" of physical proximity separate them from the nearest known case, creating a positive incentive loop where users protect themselves by installing it — a distinction he likens to free-market mechanism design versus centralized, coercive quarantine enforcement. Technically, the app uses Bluetooth proximity (not GPS) sampled every few minutes to build a sparse contact network (most people have on the order of 100 meaningful contacts), and Loh credits his and his team's competitive-programming background for engineering linear-time algorithms and efficient backend infrastructure (including a custom C++ server) that could scale to national populations without requiring prohibitively expensive server capacity. He emphasizes NOVID never asks users to quarantine and preserves anonymity (verification of positive cases requires codes issued by partnering local health authorities, since fully anonymous self-reporting would be gameable), and describes ongoing efforts to partner with epidemiologists and public health researchers — including in lower-resource countries — to validate whether the approach can help control future pandemics, particularly given the likelihood of needing periodic vaccine updates.
On the International Mathematical Olympiad, Loh explains the format (six proof-based problems over two days, four and a half hours per day, partial credit awarded through a negotiation process between country delegations and host-country graders) and reflects on the Soviet Union's historical prioritization of mathematical training as a matter of national pride comparable to Olympic sports — arguing, contra the assumption that this requires authoritarian mobilization, that the underlying idea (that "being a good thinker and creator of ideas is a good thing," sent as a message to essentially everyone) generalizes and could work in any society, pointing to America's own broad embrace of youth sports training intensity as a comparable model. He describes his own coaching philosophy as explicitly not focused on winning per se, but on maximizing how many of the students he works with go on to have significant, generalizable impact decades later — a philosophy he says was endorsed by the Mathematical Association of America when he was appointed head coach in 2013.
Discussing the nature of hard problems, Loh proposes that problem difficulty is roughly proportional to the number of discrete "leaps of insight" (reframings or applications of new tools) required, rather than sheer complexity — noting he taught himself advanced math by reading a theorem statement and the length of its proof, then closing the book and attempting to reconstruct the proof himself, using proof length as a rough proxy for the number of necessary insights. He credits his PhD advisor (Benny Sudakov) and colleague Jacob Fox with the related principle of choosing problems not just for whether they can be solved, but for whether solving them would matter or yield reusable tools — a philosophy he says directly motivated his decision to redirect his research network-theory expertise toward pandemic response. On the philosophical question of whether mathematics is discovered or invented, Loh leans toward "discovered," reasoning that concepts like circles and pi seem likely to be independently rediscovered by any sufficiently advanced intelligence (human or alien) engaging with a shared physical universe.
He also discusses two of his own research results in accessible terms: a "voting tree" tournament-circuit design problem (showing that with 1,024 candidates in head-to-head matchups, a well-designed bracket can guarantee the winner has beaten at least a near-optimal fraction of competitors, improving prior bounds from logarithmic to square-root order), and a distributed "stochastic coalescence" algorithm for parallel summation (where individuals randomly delegate partial sums to each other without central coordination), explaining how a naive implementation can develop slow, dominant "lumps" that create bottlenecks, and how a small tweak (preferring to merge with smaller rather than random lumps) restores efficient scaling — drawing an explicit connection between this delegation structure and potential models for liquid/representative democracy. Asked to speculate on P vs. NP, he defers to specialists (citing Scott Aaronson's informal "3%" estimate that P=NP) rather than offering a personal view.
He closes with advice emphasizing lifelong "invention" practice over rote learning (recommending state-level math competition problems, such as MATHCOUNTS or AMC, as accessible practice even for adults), the value of teaching a skill to solidify one's own understanding of it, and framing his personal sense of meaning around maximizing the cumulative "person-years" of impact his ideas have on others after he's gone — a metric he says he revised after realizing a widely-used simplification (of the quadratic formula) might already have nontrivial durable impact, leading him to weight impact by both audience size and duration of use per person, and to consciously prioritize working on "big enough," high-effort-required problems over comfortable, safe ones.
Excerpts
On NOVID's core reframing of contact tracing:
“The idea was: suppose there was a pandemic — what would you want? You would want a way to be able to live your life as much as possible and avoid getting sick. Can we make an app to help you avoid getting sick? Notice how I've just articulated the problem — it is not 'can we make an app so that after you are around somebody who's sick, you can be removed from society.'”
On what makes a math problem hard:
“I could quantify it by the number of leaps of insight, of changes of perspective, that are along the way... a three-insight problem is not three times as hard as a one-insight problem... The way I taught myself math was: I would look at the theorem statement, look at the length of the proof, then close the book and attempt to reprove it myself.”
On his personal measure of a meaningful life:
“I wanted to maximize a certain score, which was: for how many person-years after I'm no longer here did what I do matter... it didn't matter if it's necessarily attributed to me — it's just, did it matter.”