A Primer of Infinitesimal Analysis
A Primer of Infinitesimal Analysis by John L. Bellby John L. Bell
Shares rank 14 of 20 mathematics textbooks by recommenders
Recommended as an introduction to smooth infinitesimal analysis, which one commenter calls a better system for developing calculus. Critics say its intuitive arguments are only heuristics.
Recommended as an introduction to smooth infinitesimal analysis, which one commenter calls a better system for developing calculus. Critics say its intuitive arguments are only heuristics.
3 people gave an opinion
- recommend it
- 3
- 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: not 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: recommended
- November 2026: not recommended (month in progress)
Why it doesn’t carry the badge
- 3 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
Better system for developing calculus
“It's a much better system to develop calculus on.”
Comment from 15 Aug 2026 in “Simplifying and Refactoring Introductory Calculus” “best take is Smooth infinitesimal analysis”
Comment from 25 Oct 2026 in “I don't understand quantum physics (2018)”
What people warn about
Each mark is one comment
Intuitive arguments are only heuristics
“The seemingly very intuitive arguments in Bell's book "a primer of infinitesimal analysis" are only heuristics.”
Comment from 18 Aug 2026 in “Simplifying and Refactoring Introductory Calculus” Presented as rigorous but heuristic
“The book is written as if the intuitive arguments were actually rigorous; what's heuristic about them?”
Comment from 19 Aug 2026 in “Simplifying and Refactoring Introductory Calculus” “the proofs in the book are like that too”
Comment from 16 Aug 2026 in “Simplifying and Refactoring Introductory Calculus”
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 | — | — |
| A Primer of Infinitesimal Analysisby John L. BellThis page | 3 | 0 | 100% | 2 | — | — |
What people said
All 5 comments that mention it, newest first. Each links to the original comment.
“best take is Smooth infinitesimal analysis”
“The book is written as if the intuitive arguments were actually rigorous; what's heuristic about them?”
“The seemingly very intuitive arguments in Bell's book "a primer of infinitesimal analysis" are only heuristics.”
“the proofs in the book are like that too”
“It's a much better system to develop calculus on.”
Counts come from 1,795,640 Hacker News comments, November 2025 to November 2026. How we count. Report a mistake.