Measurement

What Hacker News says

1. _muAug 2025
   Agree, hopefully this insight / attitude will become more and more prevalent.

   For anyone looking for resources, may we recommend:

   * The Art of Doing Science and Engineering by Richard Hamming (lectures are available on YouTube as well)

   * Measurement by Paul Lockhart (for teaching mindset)

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2. suranyamiDec 2024
   “Measurement” by Paul Lockhart, of “A Mathematician’s Lament” fame.

   This was recommended by the delightful and talented Tibees YouTuber.

   A few pages in and I was absolutely hooked and ready to start proving geometric conjectures…

   A truly amazing communicator and educator.

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3. suranyamiDec 2024
   Not a course, as such, but reading “Measurement” by Paul Lockhart, of “A Mathematician’s Lament fame.

   I’ve never read anything that so clearly communicates and leads you into a state of mind that COMPELS you to prove mathematical conjectures from first principles.

   I found myself furiously sketching geometric proofs and simplifying algebraic conundrums with an enthusiasm I haven’t experienced in decades.

   And a course on sewing for beginners and continuing Japanese.

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4. sethpurcellNov 2024
   Given the sentiment in these comments, I figure this crowd might be interested in the book "Measurement" by Paul Lockhart (the guy who wrote "A Mathematician's Lament")

   He's of the opinion that math should be taught not as jumping through hoops for "reasons", but as an art, enjoyable for its own sake, and that this would actually produce more confident and capable thinkers than the current approach. (I think the argument applies to almost all education but his focus is just on math.)

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5. pbrowne011Sep 2024
   Paul Lockhart's "A Mathematician's Lament" [1] is the work that inspired his book, "Measurement" [2], which this video covers. I've always enjoyed it as a portrayal of the yin and yang of mathematics, calculating equations vs. proving them. The American education system overindexes on calculations, which, as Lockhart points out, tend to drown out the deeper joy that comes with mathematics. It's fascinating to see the battle between rote calculation and discovery play out at all levels, from students who feel that they "don't get math", to former olympiad medalists who struggle in graduate school.

   [1] https://www.ams.org/notices/201304/rnoti-p461.pdf

   [2] A preview: https://www.hup.harvard.edu/file/feeds/PDF/9780674067349_sam...

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6. _ktndJan 2024
   Below is a list of resources that I personally like, because most of them emphasize derivations/motivations (e.g., deriving the cross product out of 3 assumptions/axioms) over (mechanical) memorization (e.g., just showing the mechanics of matrix multiplication/determinants without derivations/motivations):

      - Bari A., Algorithms, YouTube (playlist),
     https://www.youtube.com/playlist?list=PLDN4rrl48XKpZkf03iYFl-O29szjTrs_O
   
     - Frenkel E., UC Berkeley: MATH 53 - Multivariable Calculus with Edward Frenkel, YouTube (playlist) https://www.youtube.com/playlist?list=PLaLOVNqqD-2GcoO8CLvCbprz2J0_1uaoZ
   
     - Hower V., Linear Algebra Full Course, YouTube (playlist), https://www.youtube.com/playlist?list=PLpcwHaLYiaEXW5fLNOlItPH4ATorKjBuc
   
     - Lockhart P., Measurement
   
     - Axler S., Linear Algebra, Springer, 2024, https://link.springer.com/content/pdf/10.1007/978-3-031-41026-0.pdf
   
     - Ström et al., Immersive Linear Algebra, https://immersivemath.com/ila/index.html (online book)
   
     - Margalit et al., Interactive Linear Algebra, https://textbooks.math.gatech.edu/ila/ (online textbook)
   
     - Macdonald A., Linear and Geometric Algebra
   
     - Macdonald A., Vector and Geometric Calculus
   
     - Ramirez et al., From Vectors to Geometric Algebra, 2018, https://doi.org/10.48550/arXiv.1802.08153
   
     - Hertzmann et al., Computer Graphics Lecture Notes, Computer Science Department - University Toronto, 2005, https://www.dgp.toronto.edu/~hertzman/418notes.pdf
   

   Further, see Sergey Trail's "Linear Algebra Done Wrong" and watch Grant Sanderson, Easy Theory (theoretical CS), Jacob Sorber (operating systems), Graphics in 5 Minutes, Sam Buss (computer graphics), Dr. Daniel Page (theory of computation, data structures and algorithms), First Principles of Computer Vision on YouTube.

   Mr. Hertzmann has some more resources (that I haven't checked out yet):

   https://www.dgp.toronto.edu/~hertzman/research.html

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