Top all-time · #111
BetterExplained
Personal blog · betterexplained.com · on HN as kalidmathscience
BetterExplained is a personal blog at betterexplained.com about math and science. Since 2007, 330 different Hacker News readers have linked it 531 times, most often “BetterExplained: Clear, intuitive lessons about mathematics”. The last post was in 2022, but the archive is still widely read.
Often recommended · 28 of 40 sampled comments recommend it?
Why HN links it
HN readers link BetterExplained to build intuition for math and calculus before the formulas. Several call it the most useful free resource they have found for understanding math.
- Recommended for · 28 comments
- Builds intuition for math and calculus; called 'excellent', 'amazing', and 'the most transformative free resource'.
Summarised by Claude from a sample of 40 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
BetterExplained teaches math the intuitive way: clear, visual lessons on imaginary numbers, exponents, calculus, trigonometry and more, with an Aha! moment before the details.
Most-linked posts?
- BetterExplained: Clear, intuitive lessons about mathematics28 people · 29 mentions · first linked 2016-08-02
- An Interactive Guide To The Fourier Transform18 people · 18 mentions · first linked 2012-12-20
- Colorized Math Equations13 people · 14 mentions · first linked 2017-12-13
- An Interactive Guide to the Fourier Transform (2012)13 people · 14 mentions · first linked 2016-11-22
- Quake's Fast Inverse Square Root12 people · 12 mentions · first linked 2008-06-10
- BetterExplained: Math Lessons That Explain Concepts12 people · 12 mentions · first linked 2009-11-19
- An Intuitive Guide to Linear Algebra11 people · 11 mentions · first linked 2012-10-09
- Intuitive Understanding of Euler’s Formula10 people · 13 mentions · first linked 2016-09-22
- Complex numbers have never been so intuitive to me10 people · 10 mentions · first linked 2007-12-21
- An Intuitive (and Short) Explanation of Bayes’ Theorem9 people · 9 mentions · first linked 2017-03-13
What Hacker News says?
I'm in a similar situation. I'm having to learn linear algebra,calc,basic prob, and brush up on all of my holes in between. I haven't found a direct path, however. What has helped me is this deep learning book[0] which has spelled out very plainly what I need to learn. From there I use a combination of math is fun[1], better explained[2] and 3blue1brown. math is fun really helps by just giving you examples and defin…
Comment linking /
on “Mathematics for the Adventurous Self-Learner”Submitted An Intuitive Guide to Linear Algebra (2012) as a story · 709 points
HN discussionSummer of 1980, going into my senior year in high school, I mentioned I'd be taking Calculus next year to a co-worker a couple years older than I. He said he had the best book in the world on Calculus, and he loaned me his copy of Silvanus P Thompson's Calculus made easy . I thoroughly enjoyed that book, benefited from its intuitive explanations, and forever appreciated his recommendation. If I may similarly influen…
Comment linking /
on “Calculus Made Easy (1914) [pdf]”Submitted BetterExplained: Math Lessons That Explain Concepts as a story · 666 points
HN discussionhttps://betterexplained.com/ is hands-down the most transformative free resource for understanding math I've ever encountered.
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on “Mathematics for Computer Science [pdf]”Submitted Math Intuition Cheatsheet as a story · 478 points
HN discussion> And if the audience, who includes both students and teachers, isn't qualified to judge the quality of the work, who exactly is? Again, it is very unfortunate, but on the average, high school teachers wouldn't be. For starters, linear algebra (where multiplication belongs) simply isn't taught at high-school level. It is not in the standard math curriculum in any state. Bits and pieces of linear algebra, like teachi…
Comment linking /articles/linear-algebra-guide/
on “Matrix Multiplication”Submitted Calculus Learning Guide as a story · 472 points
HN discussionAs others have mentioned, many introductions to linear algebra / matrix multiplication only gives the student a formula, but not why the formula looks like it does. Why is matrix multiplication not pointwise, was something I had a hard time understanding. Better explained has a good article on this, that really made it click for me https://betterexplained.com/articles/linear-algebra-guide/
Comment linking /articles/linear-algebra-guide/
on “Matrix Multiplication”Submitted Convolution Is Fancy Multiplication as a story · 397 points
HN discussion"In a room of just 23 people there’s a 50-50 chance of at least two people having the same birthday. In a room of 75 there’s a 99.9% chance of at least two people matching." https://betterexplained.com/articles/understanding-the-birth...
Comment linking /articles/understanding-the-birthday-paradox/
on “I found two identical packs of Skittles among 468 packs”Submitted What to know about the stock market (2007) as a story · 394 points
HN discussionThis is a slightly different response from others, but I think fits the intent of the question: The Better Explained Guide to Calculus: https://betterexplained.com/calculus/ Kalid basically iterates the series around the concept of deriving the formula for the area/perimeter of a circle, and then builds up to deriving the surface area/volume of a sphere. The focus throughout is the building up of an intuition of cal…
Comment linking /calculus/
on “Ask HN: What are some books where the reader learns by building one project?”Submitted An Intuitive Guide to Linear Algebra as a story · 371 points
HN discussionThis has helped many people I know get some "clicks" on a variety of topics: https://betterexplained.com/
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on “Ask HN: Do you recall any book or course that made a topic finally click?”Submitted BetterExplained: Clear, intuitive lessons about mathematics as a story · 340 points
HN discussionI have really enjoyed reading some of the better explained pages. I wouldn't recommend most people start on calculus on that site, but since you requested it specifically here's the overview: https://betterexplained.com/guides/calculus/
Comment linking /guides/calculus/
on “A visual proof that a^2 – b^2 = (a + b)(a – b)”Submitted The Rule of 72 (2007) as a story · 323 points
HN discussionI like this view of the integral (and generally regard this site as helpful to build intuitions). https://betterexplained.com/articles/a-calculus-analogy-inte...
Comment linking /articles/a-calculus-analogy-integrals-as-multiplication/
on “Calculus Made Easy”Submitted An Interactive Guide to the Fourier Transform (2012) as a story · 301 points
HN discussionSee https://betterexplained.com for that kind of "made easy" intuition-building / common-sense -oriented material.
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on “Calculus Made Easy”Submitted A Programmer’s Intuition for Matrix Multiplication as a story · 299 points
HN discussion> when people talk about safety, it does matter in Rust, right? I'm not sure I would make this about languages. Different languages have different advantages, but there's always a trade-off, right? For example, this `cp` issue is a bit of a problem for the coreutils rewrite[0]. I think you gotta ask the question: what benefit does rewriting in rust provide? Potentially more safety, but also something like coreutils…
Comment linking /articles/understanding-quakes-fast-inverse-square-root/
on “The AI coding trap”Submitted An Intuitive Guide to Linear Algebra as a story · 285 points
HN discussionGood question. I see the site as a complement to existing lesson plans. Some teachers have taken the material and presented it in their own style, which I absolutely love: Article: http://betterexplained.com/static/articles/a-quick-intuition... Video a teacher made: https://www.youtube.com/watch?v=zBYs6ppuMSk I don't know anything about educational policy, classroom management, etc. I want to provide the best ingred…
Comment linking /static/articles/a-quick-intuition-for-parametric-equations/
on “BetterExplained: Math Lessons That Explain Concepts”Submitted Learn difficult concepts with the ADEPT method (2014) as a story · 270 points
HN discussionKalid, I have a question, but first a compliment :) I am enamored with this site. It validates a lot of my learning approaches and is helping me now when I was asking some of these 'how to learn' questions. Thank you! The question: In my experience, 'generalized overview to specific' is too much required attention span for some listeners when trying to explain; Do you have a recommendation for being able to convey i…
Comment linking /static/articles/adept-method/
on “BetterExplained: Math Lessons That Explain Concepts”Submitted Intuitive Understanding of Euler’s Formula as a story · 267 points
HN discussionThanks for the feedback! The book is more of a "top concepts I wish I knew" but not really a ground-up tutorial. For starting from a clean slate, you might like: http://betterexplained.com/static/articles/rethinking-arithm... Once you can visualize the basic operations (add, subtract, multiply, divide), every new math operation becomes a lot easier (complex numbers = rotations, exponents = growth, combining them = o…
Comment linking /static/articles/rethinking-arithmetic-a-visual-guide/
on “BetterExplained: Math Lessons That Explain Concepts”Submitted An Intuitive Guide to Linear Algebra as a story · 261 points
HN discussion
