Secrets of mental math
by Arthur Benjamin · first published 2006
80% recommend20% neutral
Why HN recommends it
Practical, trick-based guide to fast mental arithmetic and calculation shortcuts. It serves as an accessible starting point for beginners and helps sharpen everyday number sense.
Summarised by Claude from recommending comments
These simple math secrets and tricks will forever change how you look at the world of numbers.Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends--and yourself--with incredible calculations you never thought you could master, as renowned "mathemagician" Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and--maybe for the first time--make mathematics fun.Yes,
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Follow that up with his slightly more advanced The Art of Insight in Science and Engineering [0]. I feel like these two books plus Art Benjamin's Secrets of Mental Math [1] would put your Fermi calculation abilities on another level. [0] https://mitpress.mit.edu/books/art-insight-science-and-engin...
on “Street-Fighting Mathematics” ↗…hard problems when you're not handed a nice formula to plug things into. Once a week, we work through a hard problem using the method in this book. 4. I haven't worked it in yet, but Arthur Benjamin's "Secrets of Mental Math" has a lot of stuff in it that will solidly connect arithmetic and algebraic thinking later.
on “Five-Year-Olds Can Learn Calculus (2014)” ↗Two excellent books on the subject are Secrets of Mental Math by Arthur Benjamin (for beginners) and Dead Reckoning: Calculating Without Instruments by Ronald Doerfler (more advanced). The Mind Your Decisions blog (http://mindyourdecisions.com/blog/tag/mental-math/)…
on “The Dying Art of Mental Math Tricks” ↗Worth a read: "Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks" by Arthur Benjamin, one of my wife's college professors.
on “Tips to Improve Your Mental Math Ability” ↗No one switched it around, that's my point. The digit order everyone uses is the one best suited to mental arithmetic in LTR languages, where the most significant digit is first. See the book Secrets of Mental Math by Arthur Benjamin. It's also the best suited to getting a rough idea of the number quickly in LTR languages. That's because the digit order everyone uses was designed for LTR languages.
on “Eid Mubarak” ↗A great book for this is "Secrets of Mental Math" by Benjamin and Shermer [0]. I remember a feeling of fun when I memorized the tricks many years ago, but unfortunately I lost the digital flash card deck for reviewing them, so I've forgotten them now.…
on “Why are mathematicians so bad at arithmetic? (2017)” ↗…sure if that's due to the readers or their teachers nostalgia or well founded yet. - The Manga Guide to Calculus Erm, yeah. (I did like the Manga Guide to Databases, though) - Benjamin & Shermer - Secrets of Mental Math How to do mental arithmetics quickly. Good for igniting the spark and impress your friends… Also, some book on mathematics by Russian, who employ some different methods in teaching, but I can't find…
on “Ask HN: How to get good at math if you are too bad with math” ↗…everyone seems to be trying to bullshit everything. I find it very difficult to find the facts on most things. But when I saw that Khan Academies methods were starting to mirror "The Great Courses" "Secrets of Mental Math"[1] and that it was a part of the common core, I was impressed. Once I started learning things this way, I was better able to handle all math. I used to hate it, dread it. But this kind of thing makes…
on “Ask HN: Common Core Math, Better? Or Worse?” ↗I highly recommend the Secrets of Mental Math book: http://a.co/095nXaa Lots of good insights on how to make shortcut mental calculations.
on “Russian Peasant Multiplication” ↗…https://math.ucr.edu/~res/math138A-2012/polya.pdf There are other books that train folks on how to do mental mathematics like * The Trachtenberg Speed System of Basic Mathematics https://www.abebooks.com/products/isbn/9780285629165/3011837... * Secrets of Mental Math https://www.abebooks.com/products/isbn/9780307338402 I found this neat publication from the American Mathematical Society on Back of the Envelope calculation. https://www.ams.org/publications/TEXT-33-chap-1.pdf
on “What use is mental math in 2022?” ↗…have been trying to go back and re-take so to speak, everything from basic algebra onwards. It struck me that my mental math chops were appalling. I've stumbled on a recommendation, here i think, of "Secrets of mental math" by Benjamin and Shermer...and goodness, as the book states several times - "why is this not taught in schools!" i mean, folks constantly say "when will i need this"...well, in my opinion, all the time...strikes…
on “Why is the state of mathematics education so abstract and uninspiring?” ↗This looks very cool, though it looks inconvenient for multiple problems due to the amount of drawing involved. A good, practical approach I've liked to use are the techniques in Benjamin and Shermer's "Secrets of Mental Math." One of the examples in the linked article shows a method of drawing for solving 42 * 21. But this is easier to solve mentally by converting this to a simpler problem, as recommended by the book: 42…
on “Japanese multiplication method and other ways to multiply (2020)” ↗Arthur Benjamin's book Secrets of Mental Math has similar tricks to this one. One I like is multiplying 10x+y by 10x+z where y+z = 10, then the answer is 100x(x+1) + yz (such that the two multiplications can be concatenated). So 53*57 = [5*(5+1)][3*7]…
on “Early Times (Multiplication)” ↗Have you used it much? I'd like one, but I can imagine it sitting on my desk for years unused. I have "Secrets of Mental Math" by Arthur Benjamin and have wanted to practice some of those mental math skills, and I wonder if learning the soroban will interfere with my existing mental calculation framework (which is admittedly…
on “The Lost Art of Logarithms” ↗I wasn't able to find anything like it online, so I thought it may be useful for the hackers out there with kids. I'm reading the book "Secrets of Mental Math", and the exercises they present are basically what this tool outputs... basic, random, arithmetic problems. So yeah, I actually created these for myself, not my kids :) Tool: http://www.elctech.com/math/random-arithmetic-worksheets-generator…
on “Learn HN: Arithmetic Sheets for Parents/Teachers with Kids” ↗