Elements

What Hacker News says

1. KvarnekSep 2026
   Always fascinated by how foundational math concepts built up. Euclid's Elements still blows my mind for its logical rigor.
   thread
2. vharuckSep 2026
   For the majority of math history, people wrote proofs using natural language. Formalized notation is relatively recent. I have read both, and the notation is (on the whole) so much easier to read. But anybody is free to learn math beyond an undergraduate level with natural language texts. If you want to be traditional, start with Euclid's "Elements."

   Plus, in the good articles I've read, the structure is usually: dissection of subproblem, intuitive description of solution, converting that solution into notation, proceed to next subproblem. If you see an unfamiliar symbol in an article, look it up. If you don't understand its definition, you don't yet have an intuitive grasp of the concept. Keep going down that rabbit hole until you have the intuitive building blocks to understand the article.

   Frankly, I love how much math we can teach before a kid graduates high school. Thousands of years of mathematical ideas, up to calculus invented less than 400 years ago. All before they're 18 years old and probably don't care much about math.

   Show morethread
3. tmtvlJul 2026
   But you can read the books as often as you want as long as you live and pass them on to your children and your children's children,...

   Educational books are an investment in the future, and some (like Euclid's Elements) don't ever lose their relevance.

   thread
4. adrian_bMay 2026
   I believe that the only useful form of the antique books, such as those originally written in Latin or Ancient Greek, is a bilingual edition, like those provided by the Loeb Library collection.

   For Euclid's Elements, there is this excellent and free bilingual edition due to Richard Fitzpatrick:

   https://farside.ph.utexas.edu/Books/Euclid/Euclid.html

   The bilingual editions are useful even for people who do not know and do not intend to learn the original language, because they still allow them to discover which were the original meanings of many old words that are still in use today and to investigate the real meaning of certain paragraphs of interest, where an English translation may be unable to provide the correct meaning, without a very long commentary about the context. Moreover, in the case of books like those of Euclid, an non-specialist translator, i.e. a non-mathematician, will frequently make mistakes that can be discovered by a specialist, i.e. mathematician, who can compare the original and the translated text, even when the specialist has only little knowledge about the ancient language.

   From Euclid's Elements, I consider that there are 2 sections that have retained most of their importance until today, and which are the most instructive: the 2 sections with definitions, the first with the definitions used in plane geometry (in Book 1) and the second with the definitions used in solid geometry (a.k.a. stereometry) (in Book 11). An important part of the mathematical language still used today has its origin in these 2 sections of definitions. There are also other 2 sections with definitions, about numbers (i.e. natural numbers) and about magnitudes (i.e. non-negative real numbers), which however have been less preserved in the modern terminology.

   Show morethread
5. ofconsequenceDec 2025
   > The Bible ... it's probably the most consequential piece of literature ever written.

   Even if you really dial in your definition of "consequential", ie. the amount of stagnated technological and societal progress and murder as a result of the Bible's adherents' efforts, this seems an absurd claim.

   Most consequential piece of literature is likely the Plimpton 322 or Euclid's Elements or The Epic Of Gilgamesh. The Bible is an embarrassing footnote.

   Show morethread
6. dkhenryNov 2025
   When I recently switched jobs, one of my requirements was I had to remain remote, for at least the next few years, so I could remain at home and help with my children's education. I don't think there is enough money in the world to convince me to change back to public education. Aside from the benefits everyone mentions like a much better education, having so much extra time with my children is a priceless gift that I wish we as a society could give everyone.

   Also its given me the chance to learn things that I missed during my primary and secondary educations. Going through each proof in Euclid's Elements again has been a lot of fun, and its been long enough that I have forgotten most of them, so the thrill of discovery is real for me too.

   If you can make it work, you should make it work, even if that means moving to a lower CoL area, there are a lot of small towns in the US that have excellent amenities, and are great places to raise a family.

   Show morethread