Name: Mathematics for the Nonmathematician
ISBN: 9780486248233

Mathematics for the Nonmathematician

Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.

What Hacker News says

codesukiMar 2025

I recently read mathematics for the nonmathematician. https://www.goodreads.com/book/show/281821.Mathematics_for_t...

Although the math in the book is relatively basic I enjoyed it tremendously because it gives the historical development for everything and even describes the characters of different mathematicians, etc. The historical context helps so much with understanding.

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SoleilAbsoluMar 2025

I was going to say the same! I got it years ago, it's hard to top a math book with a quote from a certain Al Einstein on the back cover singing its praises! Morris Kline's "Mathematics for the Nonmathematician" takes a similar approach, as I believe other books by the author do. Can also recommend "Code" by Charles Petzold and "The Information" by James Gleick, while not comprehensive they do cover the development of key mathematical insights over time.

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rootforceNov 2022

I’m a fan of Mathematics for the Nonmathematician [1]

[1] https://a.co/d/grHB5he

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meieo0Oct 2019

Mathematics for the Nonmathematician https://www.amazon.com/dp/0486248232

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jointpdfJul 2019

First of all, good on you for going back to school—that’s not always an easy thing to do. What subject are you considering studying?

Khan Academy is definitely the best one-stop-shop for this purpose, as someone mentioned. The key is to consistently do lots of practice problems over time. KA is adaptive+gamified, and helps select problems in your “zone of proximal development” (not too easy, not too hard).

Depending on what you want to get a degree in, you can focus on particular areas and gloss over others. If CS, then discrete mathematics and logic are the most important (plus stats/probability/linear algebra for machine learning and AI). If engineering, then trigonometry/calculus/physics is more important.

Learning also requires motivation, which for me personally requires seeing the big picture of why the math theory matters and how it was developed. Read the NYTimes series by Steven Strogatz. I also like “Mathematics for the Nonmathematician” for an overview of HS-level math that weaves in historical context (e.g. how Renaissance art or agriculture and mathematics are intertwined). Watch some YouTube videos on mathy subjects (like Numberphile or 3Blue1Brown or any of the zillions of channels along these lines). I try to do this as a “learning by osmosis” sort of activity that I fit in to my daily routine, e.g. when folding laundry or commuting.

Learning is also a social activity, so maybe enroll in a community college course or find a local study group. I find it’s especially important to have someone to discuss things with when learning math. I also recommend finding good public spaces to work in—libraries and coffee shops are timeless math spaces.

Along those lines—as you’re learning/reading/practicing new concepts, imagine explaining them to someone else (Feynman method).

Do lots of problems by hand on pen and paper, there is research and eons of practical experience that shows that doing math is a kinesthetic experience (that is, there’s literally “muscle memory” for math). Draw pictures and graphs on paper. Keep all this scratchwork and doodles and stuff in a notebook.

Learn to process the “I have no idea what’s going on” thoughts and feelings you get when you’re faced with something new and challenging, or seem to continually forget things you’ve just (re)learned. That’s par for the course, you just have to “feel the burn” and keep going. Cheesy but extremely true.

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dmixJun 2017

A good entry point are one of these books which start from the very beginning of math in Egypt/Greece and teach the fundamentals of math through a narrative as humans discovered the various parts:

"Mathematics for the Nonmathematician" https://www.amazon.com/Mathematics-Nonmathematician-Morris-K...

"Mathematics for the Million" https://www.amazon.com/Mathematics-Million-Master-Magic-Numb...

Of the two I prefered Kline's book but they are both good, albeit a bit heavy on geometery as that was a big focus of early math research.

Another great starting point is "Book of Proofs" and "Introduction to Mathematical Reasoning" to give you a deeper sense of how to approach the subject.

https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472...

https://www.amazon.com/Introduction-Mathematical-Reasoning-N...

From there I went down this path (the order of which is up to you, each has tons of good source material):

-> Proofs/Logic

-> Algebra

-> Linear Algebra

-> Calculus

-> Abstract Algebra

-> Set Theory

-> Group Theory

-> Category Theory

-> Statistics/Probability

-> Discrete Mathematics

I never did well with learning math in a classroom but I've grown to love math through this process. There are lots of applications in programming as well. It makes approaching the deeper parts of Haskell/FP, data science, and machine learning much more accessible. I particularly liked the higher level Abstract Algebra stuff over the more grinding equations of calculus/linear algebra as it was more similar to programming.

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