Homotopy Type Theory
Homotopy Type Theory by the Univalent Foundations Programby the Univalent Foundations Program
Shares rank 7 of 20 mathematics textbooks by recommenders
People recommend it for explaining type theory and mind-altering ideas like higher inductive types. One mixed review says the second chapter is hard to follow.
People recommend it for explaining type theory and mind-altering ideas like higher inductive types. One mixed review says the second chapter is hard to follow.
4 people gave an opinion
- recommend it
- 4
- criticize it
- 0
- approval share
- 100%
Recommended in 2 of 13 months
- November 2025: not recommended
- December 2025: not recommended
- January 2026: not recommended
- February 2026: recommended
- March 2026: not recommended
- April 2026: not recommended
- May 2026: not recommended
- June 2026: not recommended
- July 2026: not recommended
- August 2026: recommended
- September 2026: not recommended
- October 2026: not recommended
- November 2026: not recommended (month in progress)
Why it doesn’t carry the badge
- 4 people recommend itNeeds 10 or more, not met.
- Nobody criticizes itNeeds 2 to 1 or better, met.
- Recommended in 2 of 13 monthsNeeds 4 or more, not met.
The same three rules apply to every product, and the badge can’t be bought. How the badge works
What people say about it
The reasons people give, with the number of comments that give each one. Open a reason to read what they said.
Why people recommend it
Each mark is one comment
Easy-to-follow first chapter
“First chapter on type theory is great and pretty easy to follow. The second chapter, I got completely lost.”
Comment from 13 Aug 2026 in “Principia Mathematica is modern and insightful” Helpful for understanding core concepts
“HoTT is a really helpful way to better understand those concepts.”
Comment from 13 Aug 2026 in “Principia Mathematica is modern and insightful” Clarifies mere propositions
“Mere propositions is probably best viewed with Homotopy Type Theory”
Comment from 18 Feb 2026 in “Learning Lean: Part 1” Mind-altering higher inductive types
“higher inductive types are downright mind-altering”
Comment from 13 Aug 2026 in “Principia Mathematica is modern and insightful”
What people warn about
Each mark is one comment
Second chapter is hard to follow
“First chapter on type theory is great and pretty easy to follow. The second chapter, I got completely lost.”
Comment from 13 Aug 2026 in “Principia Mathematica is modern and insightful”
Other mathematics textbooks people recommend
The four most recommended other mathematics textbooks, with the same counts for each, so you can compare like for like. The tick on each bar marks the 2 to 1 line the badge needs.
| Product | Recommend | Criticize | Approval | Months | Owned | Badge |
|---|---|---|---|---|---|---|
| Algorithms for Optimizationby Kochenderfer and Wheeler | 10 | 1 | 91% | 1 | — | — |
| Mathematics for Computer Scienceby Lehman, Leighton and Meyer | 8 | 4 | 67% | 1 | — | — |
| Numerical Recipesby Press et al. | 7 | 1 | 88% | 5 | — | — |
| Concrete Mathematicsby Graham, Knuth and Patashnik | 7 | 0 | 100% | 4 | — | — |
| Homotopy Type Theoryby the Univalent Foundations ProgramThis page | 4 | 0 | 100% | 2 | — | — |
What people said
All 4 comments that mention it, newest first. Each links to the original comment.
“HoTT is a really helpful way to better understand those concepts.”
“First chapter on type theory is great and pretty easy to follow. The second chapter, I got completely lost.”
“higher inductive types are downright mind-altering”
“Mere propositions is probably best viewed with Homotopy Type Theory”
Counts come from 1,795,640 Hacker News comments, November 2025 to November 2026. How we count. Report a mistake.