An introduction to mathematics

What Hacker News says

1. ivan_ahFeb 2020
   I have two recommendations that I don't see mentioned by anyone else yet:

   1. An Introduction to Mathematics by Alfred North Whitehead, 1911 available at http://www.gutenberg.org/ebooks/41568

   It not specifically about history, but I found it nice how it builds up concepts from first principles, e.g. "We had problem X, so we invented math concept Y to help with problem X, and then extended the idea concept Z that handles more general class of problems."

   2. Mathematics 1001: Absolutely Everything That Matters About Mathematics in 1001 Bite-Sized Explanations Hardcover by Richard Elwes, 2010. (non free)

   This one doesn't go into any details on any topics, but it gives you a bird's eye overview of many topics and based on the "sampling" I did for the few concepts that I know, I found the bite-size explanations to be fairly good (i.e. mathematician explains things in plain language, and not science journalist simplistic analogy).

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2. pfdietzOct 2026
   "Civilization advances by extending the number of important operations which we can perform without thinking of them."

   ― Alfred North Whitehead, "An Introduction to Mathematics" (1911)

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3. mncharityOct 2026
   > I'm not sure we have been living the dream [of software reuse]

   But would you give up packages, central repositories, downloads that Just Work without patching, public version control systems, open-source software, ... , and much of what they enabled?

   "Civilization advances by extending the number of important operations which we can perform without thinking about them." - Alfred North Whitehead, An Introduction to Mathematics (1911)

   Getting packed into 2026 airline seats can be a "miserable experience". But that taken-for-granted human flight... a cramped seat in the effin clouds... is what? A century or two of focused effort, eventually massive effort, building that dream? Another century pursuing the dream of compact mechanical power? 10 millennia on metallurgy? So one's flight may have sucked, and there are many downsides to aviation existing... but living the dream of human flight, isn't living in a dream of no problems and effortless happily ever afters.

   But yes, I'm so looking forward to agentic full-stack-ish rewrites, slashing through decades of accumulated stagnant cruft. Laptop-like angular-resolution HMDs are this-year-ish (though expensive, not mass market). And doing such rewrites by hand is a pain. Someone reports a Claude one-shot which installed a PICO Space Pro dev env, created a simple app, uploaded the apk to the headset, and responded with "ready for you to test"... and it was. Wild ride incoming. Though that's perhaps not a minimalist/efficient renaissance you had in mind? Still, in the midst of upset, there's opportunity to pursue visions which might not be viable in more settled times.

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4. jfarmerFeb 2025
   “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.”

   — Alfred North Whitehead, "Introduction to Mathematics" (1911)

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5. bikenagaApr 2024
   "It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments." - Alfred North Whitehead, "An Introduction to Mathematics", pp. 45–46
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6. amadeuspagelJan 2024
   “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.”

   ― Alfred North Whitehead, An Introduction to Mathematics

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