Mathematics for the million

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1. elzbardicoMay 2025
   You'd love a very old book named Mathematics for the Million. The author was a committed Marxist and an Engineer, and due to this combination, it places a strong emphasis on demystifying concepts, the historical context of mathematical ideas and its practical application.

   Of course, some of it is a bit strange for modern audience, the way lots of things in calculus are taught nowadays is completely different. If you are looking for rigorous formal proofs, you won't find them on this book.

   But it is a quite funny and quirk book that gives you a different perspective on math concepts and will satisfy your hunger for knowing the people and the historical context behind it.

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2. spc476Mar 2025
   There is Mathematics for the Million by Lancelot Hogben, which not only covers math, but the history of math and why it was developed over the centuries. It starts with numbers, then geometry, arithmetic, trig, algebra, logarithms and calculus, in that order. It's a very cool book.
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3. calebjosueAug 2024
   When Judea Pearl was asked how Mathematics should be taught, he answered: Chronollogicaly. [1]

   Now, What do You mean to "learn Math". You have to be more specific with your goal. This is funny coming from me because I haven't able to specialize in any single topic.

   Let's suppose You somehow saw The Beauty of Math somewhere and You are ready to continue your journey in such a beautiful topic.

   I really believe You Will enjoy reading "Mathematics for The million" by Lancelot, I saw this recommended by Sir Anthony Hoare[2], You Will be amazed by its content (I have only ready chapter one).

   What's Mathematics?

   Are elementary school children doing Math when they solve addition and subtraction problems?

   Is The High school student crunching mechanical procedures, plugging numbers into formulas doing Math?

   Is theorem proving Math?

   Daphne Koller said in an interview that we are all doing probabilistics when Thinking and making certain decisiones[3]. Are we all Mathematicians?

   Do You want to study Math as a tool to help You in some other areas or study it itself as a subject?

   It doesn't matter, You Will enjoy it and love it.

   Trying yo answer your question. Learn some Arithmetic, just enough. Crunch some elementary algebra (in The fashion of Visualizing Algebra provided by Udacity). Read The book Geometry by Tatiana Alekseyevskaya, learn some Discrete Math (I recommend You the book on the topic by Thomas VanDrunnen), read the other four books in the gelfand series. Learn some logic. Read Introduction to Mathematical Thinking by Keith Devlin. I think at this point You Will able to read some resources o calculus or abstract Algebra.

   If this seems like a Lot, don't dismay. There was this guy George Green having to take care of mill to make bread and do also found time for Mathematics, apparently DeMoivre was struggling financially. There people are just like You. Enjoy your Math journey

   [1] The interview is available on Lex Fridman YouTube channel.

   [2] The conversation between him and Leslie Lamport is available on YouTube

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4. slicktuxJan 2023
   Plus one for this! I bought two copies of the referenced book…and for the exact same reasons; I’m a programmer and being able to explain my algorithms using mathematical notation helps validate a program as well as troubleshoot a program… An oldie but goodie is “Mathematics for the million”
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5. o4tunaJan 2023
   _Mathematics for the Million_ by Lancelot Hogben.
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6. anigbrowlJun 2022
   Surprised nobody has mentioned https://pimbook.org/

   Jeremy Kun is a mathematician and programmer who has worked at Google and also maintains a blog at https://jeremykun.com/ (though he's writing another book more than he's blogging atm).

   This does a fantastic job of teaching how you read proofs, which is otherwise a very frustrating exercise for the non-mathematician. Mathematicians, he explains, write for other mathematicians rather than students, so even rigorous proofs are full of implicit assumptions and handwaves that are deeply confusing to those outside the discipline. Kun elucidates how mathematicians think and communicate, from obscure but important typographical symbols to how conceptual formation proceeds very differently from algorithmic execution - emphasizing mathematicians' goal of understanding why mathematical objects behave a certain way as distinct from observation of how they do it. He goes back and forth between picking mathematical entities and showing how they can end up as code, and looking at code that 'just works' and backtracking to explore what makes the underlying math optimal.

   It's language-agnostic and takes a slow measured approach, delving into different areas of math (calculus, linear algebra, etc) in each chapter and taking time to situate the examples in their historical and developmental context (this is foundational, that derives from the application of technique in one field to a problem in another). It's not a quick or easy read and I tend to work through a section and then set it aside while I let the insights germinate and change how I work (which is why I haven't finished it yet). But it is an enjoyable read: Kun is an engaging writer, provides useful bibliographic suggestions in context, points out blind alleys or short cuts that might not be worth taking, and reassures with stories of his own and famous mathematicians' frustrations and mistakes, so that when you inevitably run into difficulties you don't feel demoralized or stupid. The annotated bibliography in the endnotes is worth the price of admission alone.

   I was in a similar position to you of being kinda good at and enjoying math but not having a good theoretical foundation, so it would be easy to get sidetracked into problems of calculation or notation and lose sight of which techniques to reach for or appreciate how a superficially complex-looking thing is simple but being expressed very tersely.

   Other books I found worth reading over the years:

   Euclid's Elements, because you can't be too good at geometry and the proofs are so concise you can treat them as warm-up exercises

   Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid, which uses humor, poetry, art, music, philosophy as mnemonic digressions to explore one very advanced mathematical proof (Godel's incompleteness theorem) and a lot of foundational computer science concepts.

   Lancelot Hogben's Mathematics for the Million, an old-fashioned (1936) work aimed at the under- or reluctantly-educated person who wants to catch up. Much more about developing the skills to do math with pencil and paper (and perhaps a slide rule) than your original question of how to write proofs (not mentioned at all until page 60), but useful because it explores how and why different fields of math originated in practical need. If you can put up with his verbose style (and assumption that you will be working the examples by hand), he begins with the very basic questions of how to count and measure things and works (slowly) towards the demontrating things in the context where they matters - for example, theorems of spherical geometry are proven as solutions to the acute problems of ocean navigation.

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