How I Won 3 Gold Medals in the International Math Olympiad

Main ideas, concepts, and lessons

• Belief that gold is attainable

  • The guest highlights a “one word of wisdom” theme: double-check solutions—especially for functional equations—because small verification mistakes can cost points.
  • More broadly, he argues that any motivated person can reach gold in the IMO with enough effort (though the required time varies by person).

• Imposter syndrome and self-comparison

  • He often felt “not good enough”, particularly during graduate school (early research years).
  • His coping strategy is mainly to ignore the feeling and focus on learning, while avoiding excessive comparison.
  • He recommends reframing comparison as comparing to your past self, which he finds healthier than comparing to others.

• Core problem-solving mindset

  • For hard IMO problems, he agrees with an approach attributed to another top contestant: don’t treat the question as an immediate target; first understand what’s going on.
  • His “aha moments” tend to be less about raw genius and more about:
    • Recognition and reuse of known ideas (e.g., realizing the problem matches the structure of a known theorem/argument).
    • The most important breakthrough is connecting the problem to its underlying structure.

• Why understanding beats memorizing

  • It’s not enough to pattern-match solutions or just know the statements of theorems.
  • You must understand where the methods come from so you can reapply them later.

• Training approach and the gap between fundamentals and Olympiad level

  • He distinguishes between:
    1. Resource type 1: foundational tools (learn standard concepts like the pigeonhole principle, orthocenter, etc.).
    2. Resource type 2: deliberate practice at difficulty (solve contests and shortlist problems).
  • He describes a “gap” after learning basics, which is filled by immersing yourself in progressively harder problem sets.

• Role of environment, teachers, and community

  • He credits strong teachers and math camps/clubs for developing his skills.
  • He emphasizes learning from peers: hearing how others think, comparing approaches, and sometimes solving together.
  • He also stresses immersion: “live the life of solving math problems.”

• How to handle roadblocks

  • He recommends a practical balance:
    • Try to work independently first.
    • Use a time-based rule (example given: ~2 hours) before looking at solutions or hints.
    • Sometimes it’s okay to think longer (even days/weeks, especially if it genuinely interests you, and particularly in research).
  • He notes that learning from solutions may require redoing parts yourself afterward to internalize the method.

• Specific preparation resources and routines (as described)

  • He mentions:
    • Standard textbooks for foundational tools.
    • IMO shortlist problem databases.
    • National Olympiad problems (e.g., USA/American, Russian, Chinese sources).
    • Art of Problem Solving (AoPS), especially contest sections/problems.

• Functional equation verification as a decisive lesson

  • He recounts a story about losing/earning points on an IMO functional equation problem (P4) due to not explicitly checking the proposed solution.
  • His takeaway is direct: always double-check that the proposed solution satisfies the equation.

• Experiences beyond competition

  • He views IMO and mathematics as including:
    • Friendships and communication as essential parts of doing math.
    • Learning what goes on “behind the curtains” in how the event is run.
  • As a member of the IMO problem selection committee (2023), he learned how hard it is to design problems that are:
    • Accessible to students, and
    • Elegant in structure.

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Methodologies / routines / instruction-like guidance

A) Approach to tough problems (conceptual method)

• First goal: understand the problem’s structure
  • Aim to see what is going on rather than chase the final answer immediately.
• Search for underlying structures
  • Look for patterns resembling known configurations or standard transformations.
• Connect to known concepts
  • Build exposure so the problem “links” to an existing theorem/argument.
• Check understanding deeply
  • Focus on why methods work and why alternatives fail—not just on applying techniques.

B) Solving when stuck (practical workflow)

• Attempt independently first
  • It’s generally advisable to try to figure it out yourself.
• Use a fixed time threshold (example given)
  • After about 2 hours, check a solution (or at least the first part) and then attempt the rest.
• Alternative for personally engaging problems
  • If you truly enjoy the problem, it can be productive to think longer (days/weeks); in research, even longer.

C) Learning cycle (from fundamentals to contest performance)

• Step 1: learn basic tools
  • Study standard topics (examples mentioned: pigeonhole principle, orthocenter).
• Step 2: apply through progressive contest practice
  • Solve from IMO shortlist problems and other national contest sets.
  • Use an online problem platform (AoPS contests) to keep practicing at increasing difficulty.
• Step 3: internalize, don’t just copy
  • After seeing solutions, try to re-derive parts yourself to gain real understanding.

D) Verification discipline (competition-critical checklist)

• When solving functional equations (and generally whenever possible):
  • Double-check your work.
  • Explicitly verify that your proposed solution satisfies the equation—don’t assume.

E) Preparation resource suggestions (as stated)

• Foundations
  • Standard math textbooks covering core olympiad tools.
  • One named book: “Problem Solving Strategies” by Engel.
• Practice
  • Huge databases of IMO shortlist problems.
  • National olympiad problem sets (examples cited: American/USA, Russian, Chinese).
  • Art of Problem Solving (AoPS) contest sections.

F) Mindset for competition performance

• Be well-rounded
  • Don’t focus only on the problem types you prefer.
• Don’t compare to others excessively
  • Compare to your past self; comparison can steal joy.

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Speakers / sources featured (identified in the subtitles)

Speakers

• Kim Dongril / Kim Dongal (guest; IMO competitor with gold medals; Stanford graduate student; IMO 2023 problem selection committee member)
• Danielle (host/interviewer; also speaks to Kim during the podcast)

Other referenced individuals (mentioned, not as speakers in the clip)

• Ensuji / Insuji (another IMO gold medalist referenced for an approach to hard problems)
• “North Korea escapee” (mentioned by the host/guest for context; referenced as someone who escaped NK and had been at IMO 2013)