Grant Sanderson created 3Blue1Brown to explain mathematics visually and help more people appreciate its ideas. His talks and interviews explore mathematical intuition, problem-solving, teaching, and the tools behind his animations. — 3Blue1Brown About.

Infographic for "Lessons from Grant Sanderson".

On the Philosophy and Beauty of Math

  1. Math studies abstract patterns: Sanderson describes mathematics as the study of abstractions over patterns and logic, while noting that mathematicians differ in their motivations. — Lex Fridman Interview #64.
  2. Discovery guides invention: He sees a cycle in which mathematicians invent frameworks while discoveries about the world influence which frameworks prove useful. — Lex Fridman Interview #64.
  3. Apparently useless math can later matter: Sanderson observes that mathematical ideas sometimes find unexpected practical uses long after their discovery. — StarTalk Radio Interview.
  4. Let math be beautiful as well as useful: His channel explores both foundational topics and playful problems, aiming to help people appreciate mathematics for utility or beauty. — 3Blue1Brown About.
  5. Use abstraction to connect patterns: Sanderson distinguishes the abstraction and pure pattern-seeking of mathematics from physics’ direct grounding in the observable world. — Lex Fridman Interview #64.
  6. Respect symmetry: In his calculus exposition, Sanderson chooses a symmetric way to divide a circle because it makes the area argument more tractable. — Essence of Calculus.
  7. Invite wonder before utility: Sanderson argues that stories and intrinsic delight can draw learners into mathematics even when no immediate application is promised. — Math Engagement TEDx Talk.
  8. Give technical explanations a story: He asks educators to make room for characters, mystery, emotion and resolution alongside mathematical mechanics. — Math Engagement TEDx Talk.
  9. Different minds may build different math: Asked about alien mathematics, Sanderson says it could differ markedly because notation and modes of thought shape mathematical development, while counting may be broadly shared. — Lex Fridman Interview #64.
  10. Leave room for an aha moment: For Sanderson, a partly understood idea can be especially beautiful because the remaining mystery invites personal discovery. — Lex Fridman Interview #64.

On Learning and Problem-Solving

  1. Solve more problems than feels natural: He recommends spending less time only watching or reading and more focused time solving carefully chosen problems. — Best Way to Learn Math Interview Clip.
  2. Work the exercises before moving on: Sanderson advises readers to attempt some chapter problems before deciding they have learned the material. — Best Way to Learn Math Interview Clip.
  3. Rediscover to gain ownership: Sanderson says he understands ideas most deeply when he reconstructs part of them himself, though he acknowledges the approach can slow him down. — Grant Sanderson Interview #118.
  4. Let math expose limits: Sanderson recounts that studying mathematics showed him the limits of his own intuition and made him more open to learning. — Dwarkesh Podcast Interview.
  5. Preview problems before reading: He suggests glancing at end-of-chapter questions first so the reading is guided by concrete puzzles. — Best Way to Learn Math Interview Clip.
  6. Try different routes through difficulty: Sanderson says learners who persisted through hard math often changed how they learned rather than relying on unusually strong initial intuition. — Stanford Daily Event Report.
  7. Name the objects in a problem: In a problem-solving lecture, Sanderson shows how meaningful names help organize a geometry problem and make new relationships visible. — Problem-Solving Lecture.
  8. Use symmetry as a clue: Sanderson demonstrates how noticing symmetry can expose relationships hidden in an apparently arbitrary diagram. — Problem-Solving Lecture.
  9. Ask an easier version first: When a problem is too hard, Sanderson recommends simplifying it to find a foothold that can later be generalized. — Problem-Solving Lecture.
  10. Draw a representation: Sanderson turns abstract quantities into diagrams or coordinates to reveal structure that is harder to see in words alone. — Problem-Solving Lecture.
  11. Let programming motivate math: Sanderson has seen people discover an interest in mathematics through programming problems that give the subject a concrete purpose. — Best Way to Learn Math Interview Clip.
  12. Explain to consolidate learning: Sanderson and Fridman discuss active explanation or teaching as a useful way to consolidate what one has learned, without relying on numerical retention claims. — Best Way to Learn Math Interview Clip.

On Teaching and Explanation

  1. Teach for possible rediscovery: His calculus series aims to make the core ideas feel discoverable by a learner, rather than merely presenting finished formulas. — Essence of Calculus.
  2. Put visuals before formal language: Sanderson says a visual-first explanation can give learners a sense of ownership before formal meaning is articulated. — Stanford Daily Event Report.
  3. Start with motivating examples: Sanderson warns that experts are tempted to open with a general abstraction; he prefers a concrete example that earns the abstraction. — Dropbox Interview.
  4. Bring understanding out of students: Using the word “educe” as a teaching metaphor, Sanderson argues that education should draw out learners’ understanding rather than merely transfer facts. — Dwarkesh Podcast Interview.
  5. Motivation precedes explanation: He argues that friends, projects and goals often determine whether people begin learning; good explanations help once motivation exists. — Dwarkesh Podcast Interview.
  6. Educators do more than explain: Sanderson distinguishes an educator’s work of guiding interests and learning environments from the narrower task of providing an explanation. — Dwarkesh Podcast Interview.
  7. Use story in technical teaching: Sanderson says even a technical math lesson can hold attention longer when it has a narrative arc. — Math Engagement TEDx Talk.
  8. Add the story around the technology: When discussing teaching technical subjects, Sanderson stresses that conveying the narrative around an idea adds value beyond demonstrating a tool. — Grant Sanderson Interview #118.
  9. Do not talk down to learners: He argues that learners want an authentic encounter with the underlying mathematical material, not an oversimplified substitute. — Pedagogical Curse Lecture.
  10. Treat clarity as part of rigor: In his pedagogical-curse lecture, Sanderson asks mathematicians to take explanatory clarity seriously rather than assume correctness alone makes a lesson teachable. — Pedagogical Curse Lecture.

On Technology and the Future of Math Education

  1. Build tools from real teaching needs: Manim began as rough Python code Sanderson made for his own mathematical animations before it grew into a tool others used. — IAPS Interview.
  2. Keep animation programmable: Sanderson wanted animation tools flexible enough to express mathematical ideas without being confined to a graphical interface. — Advice for Using Manim Interview Clip.
  3. Use Manim where code adds value: Sanderson advises using programmatic animation for the parts that benefit from it and other tools for tasks that do not. — Advice for Using Manim Interview Clip.
  4. Online videos do not replace teachers: He says good online explanations are valuable but cannot fully provide the personal guidance and social context of a classroom. — Dwarkesh Podcast Interview.
  5. Describe AI math ability with a date: In his 2023 interview, Sanderson described AI as already useful at many mathematics tasks but short of the strongest human mathematicians; this was a time-bound assessment. — Dwarkesh Podcast Interview.
  6. Let simulation change intuition: Sanderson sees interactive simulation and programming as promising media for exploring mathematics when those tools fit the topic. — Dwarkesh Podcast Interview.
  7. Open-source a useful tool: Sanderson says he shared Manim because viewers asked how he animated his videos; community contributors later made it more accessible. — IAPS Interview.

On Creativity and Personal Growth

  1. Follow genuine curiosity: Sanderson chooses subjects that fascinate him because he believes his own interest helps convey excitement to viewers. — IAPS Interview.
  2. Start a project without growth pressure: Sanderson says 3Blue1Brown began as a low-stakes project rather than a planned large channel, which gave him room to explore. — Dwarkesh Podcast Interview.
  3. Serve the audience that wants depth: Sanderson sees demand for science and math explanations that reveal how practitioners think, not just surface-level conclusions. — Dropbox Interview.
  4. Let a personal tool become a public lesson: His first animations grew from a personal programming experiment into lessons that eventually became 3Blue1Brown. — IAPS Interview.
  5. Help more people like math: Sanderson explicitly wants more people to see themselves as liking mathematics, while distinguishing that goal from sending everyone into math academia. — Dwarkesh Podcast Interview.

Learn more:

  1. Lex Fridman Podcast #64 — Grant Sanderson and the Beauty of Mathematics
  2. StarTalk Radio — Our Mathematical Universe with Grant Sanderson
  3. Exploring the Path of 3Blue1Brown: A Conversation with Grant Sanderson - IAPS
  4. Dwarkesh Podcast — Grant Sanderson on the Past, Present, and Future of Mathematics
  5. 3Blue1Brown — About the Channel and Its Teaching Philosophy
  6. 3Blue1Brown creator Grant Sanderson '15 talks engaging with math using stories and visuals - The Stanford Daily
  7. Grant Sanderson — What Makes People Engage With Math (TEDxBerkeley)
  8. Grant Sanderson — Best Way to Learn Math (Original Interview Clip)
  9. Grant Sanderson — Math, Manim, Neural Networks and Teaching (Interview #118)
  10. Dropbox — Grant Sanderson Channels His Passion for Math into Explainer Videos
  11. Grant Sanderson — Math's Pedagogical Curse (JPBM Award Lecture)
  12. Grant Sanderson — Advice for Using Manim (Original Interview Clip)
  13. 3Blue1Brown — Tips to Be a Better Problem Solver
  14. 3Blue1Brown — The Essence of Calculus