[HN Gopher] Show HN: Exploring Mathematics with Python
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Show HN: Exploring Mathematics with Python
Author : Andrew2565
Score : 219 points
Date : 2025-12-19 15:55 UTC (6 days ago)
(HTM) web link (coe.psu.ac.th)
(TXT) w3m dump (coe.psu.ac.th)
| efavdb wrote:
| Looks like a treasure trove of knowledge.
|
| I just recently went to the exploratorium in SF and saw an
| exhibit there suggesting that the catenary made a good arch, so
| browsed that chapter and saw a bit of explanation here which
| helped. Was also interested to see that Jefferson played some
| part in the history here.
| rramadass wrote:
| Very Nice!
|
| However, I don't see the entire book as a single pdf?
| fnord77 wrote:
| I downloaded each chapter and combined them so I could read it
| in apple books on my ipad pdfunite $(ls -tr)
| "Exploring Mathematics with Python".pdf
| WillAdams wrote:
| As noted above at:
| https://news.ycombinator.com/item?id=46382915
|
| a single PDF will be provided once one more chapter is
| compleated.
| urutom wrote:
| I own the original Exploring Mathematics with Your Computer(Turbo
| Pascal version). It's an excellent introduction to algorithms for
| people coming from a mathematics background. Really happy to see
| it revived in Python.
| fnord77 wrote:
| Very nice. I was looking for something fun to work on over the
| break. Thank you for this.
|
| > Unfortunately, after lengthy discussions with the MAA, my hopes
| of publishing this (rather large) expansion have proved
| impossible, and so I've decided to put it online, hopefully to be
| of use to others.
|
| Too bad
| zkmon wrote:
| It is painful to imagine how these fantastic works will be not be
| read by humans in future, as AI would digest all this and provide
| just-in-time code for humans.
| T-A wrote:
| The kind of people who read books like this will keep reading
| them no matter what AI does. The kind of people who won't are
| already using code written and packaged as convenient libraries
| by others.
| rramadass wrote:
| You are mistaken if you think the code is the point (it is
| not); It is the Mathematics which is important. AI tools can
| help me in my studies/work but the understanding still has to
| happen in my own head.
| mettamage wrote:
| Hannah Fry said that learning math feels like gaining a 6th
| sense. That's why I continue to study it. I feel it. It's fun
| to experience the world in more ways.
|
| The same goes for Vipassana meditation.
| 0xpgm wrote:
| I believe just as human experts do peer review, someone will
| need to review the AI's work.
|
| The people who do this review will have to know enough to
| follow along.
| LenaRyouna wrote:
| People will always read things, not just because it's a
| necessity for something else, but just for fun, for curiosity,
| as a game etc.
|
| People do plenty of recreational things which don't make sense
| from an efficiency perspective; they do it because it's fun.
| robrain wrote:
| Since the dawn of the current "AI" I've continued to buy and
| read books at the same pace. Likewise downloading interesting
| human-created PDFs. I know I'm not the only human who takes
| zero interest in the output of word-sausage extruders.
| Andrew2565 wrote:
| Joint author here.
|
| I plan to upload the entire book as a single PDF when I finish
| the next chapter (on the cycloid). That will probably be early
| next week.
|
| I used the original book by Arthur Engel for many years. He was
| an inspirational teacher.
|
| The MAA tried very hard to publish the book, but I kept adding
| new material, and a text consisting of math 'selections' rather
| than a single theme is a hard sell in today's publishing
| environment.
| gostsamo wrote:
| For accessibility reasons, is it possible to have the chapters
| in html form as well? I don't know if it is possible to have
| the source code of the book, but it is also an option.
| AnotherGoodName wrote:
| On this note I'd be willing to support a html port with
| inline python code running via pyodide if the helps wanted
| too.
|
| See https://rubberduckmaths.com/eulers_theorem for an example
| where i wrote a blog post with lots of inline runnable Python
| code samples.
|
| I think this is the best format for python code samples and
| tutorials. It's even better than notebooks. No IDE to setup,
| a completely static and saveable html page, easily runnable
| and changeable python.
| rramadass wrote:
| > I kept adding new material, and a text consisting of math
| 'selections'
|
| That is what makes it so interesting to a "mathematically
| inclined" layman; a smorgasbord of Mathematics! More value for
| the time/money ;-)
|
| If MAA does not understand that there is huge market for
| Mathematics targeted towards Computer Programmers, they are
| just dumb. Programmers are the ones with the money and the
| interest in learning Mathematics presented in a manner more to
| their understanding.
|
| Please do find some other low-cost publisher to publish this;
| "Dover Publications" might be a good one since they publish a
| lot of classics particularly if you position this as a modern
| update to the Engel book.
|
| For example; John Stillwell positioned his _Elements of
| Mathematics: From Euclid to Godel_ as a sort of modern update
| to Felix Klein 's _Elementary Mathematics from an Advanced
| Standpoint._ From the preface;
|
| _This book grew from an article I wrote in 2008 for the
| centenary of Felix Klein's Elementary Mathematics from an
| Advanced Standpoint. The article reflected on Klein's view of
| elementary mathematics, which I found to be surprisingly
| modern, and made some comments on how his view might change in
| the light of today's mathematics. With further reflection I
| realized that a discussion of elementary mathematics today
| should include not only some topics that are elementary from
| the twenty-first-century viewpoint, but also a more precise
| explanation of the term "elementary" than was possible in
| Klein's day.
|
| So, the first goal of the book is to give a bird's eye view of
| elementary mathematics and its treasures. This view will
| sometimes be "from an advanced standpoint," but nevertheless as
| elementary as possible. Readers with a good high school
| training in mathematics should be able to understand most of
| the book, though no doubt everyone will experience some
| difficulties, due to the wide range of topics...
|
| The second goal of the book is to explain what "elementary"
| means, or at least to explain why certain pieces of mathematics
| seem to be "more elementary" than others. It might be thought
| that the concept of "elementary" changes continually as
| mathematics advances. Indeed, some topics now considered part
| of elementary mathematics are there because some great advance
| made them elementary..._
| efavdb wrote:
| I would certainly buy a copy were it printed!
| vector_spaces wrote:
| > If MAA does not understand that there is huge market for
| Mathematics targeted towards Computer Programmers, they are
| just dumb.
|
| Presumably a large math textbook publisher that has been
| publishing math books for literally one hundred years is very
| tapped into what books likely will and won't sell. I find it
| unlikely that a layperson where it concerns math book
| publishing would have some unique insight that MAA does not
| have. Even if there is a substantial enough market, there are
| likely unique considerations that MAA is beholden to which we
| aren't privy to
|
| I don't know what the calculus is like to get an extended
| version of an existing book published by another publisher,
| but Dover's Aurora series consists of modern original texts
| as opposed to their usual republications of classic out of
| print texts -- this is how Emily Riehl had her "Category
| Theory in Context" published
| __mharrison__ wrote:
| Impossible to self publish?
| net_rando wrote:
| Random thoughts:
|
| - Seems great. Added to the backlog :)
|
| - No colors in PDF illustrations. Is it a deliberate choice?
|
| - > The first six chapters (and Appendix A) are essentially that
| book, but with the programming language changed to Python, some
| rewording, reformatting in Latex, and a few additions.
| Try [typst](https://typst.app/) as an alternative to Latex.
| magmostafa wrote:
| This is an excellent resource for building mathematical intuition
| through code. Python's combination of readable syntax and
| powerful libraries (NumPy, SymPy, Matplotlib) makes it ideal for
| exploring concepts like linear algebra, calculus, and discrete
| math interactively.
|
| One approach I've found effective: start with a conjecture,
| visualize it with matplotlib, then prove it formally. The instant
| feedback loop helps develop both computational thinking and
| mathematical rigor. Tools like Jupyter notebooks make this
| workflow seamless.
|
| For anyone interested in similar resources, "Mathematics for
| Machine Learning" by Deisenroth et al. and 3Blue1Brown's linear
| algebra series complement this beautifully by bridging theory and
| computation.
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