Name: A concise history of mathematics
ISBN: 9780486602554

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antioedipusAug 2023

You (or others) may like Struik’s A Concise History of Mathematics [1]. It’s also quite easy to read cover-to-cover. My other favorite, Stillwell’s Mathematics and Its History, is excellent as well.

In my opinion, Stillwell’s book is better to read as a way to motivate a particular topic, whereas Struik’s book really tries to illustrate the arc of mathematics through history—of course, Struik’s approach has its limits.

History can motivate otherwise inscrutable or dry mathematics in a way that would probably interest many students. Why isn’t the history of math a serious part of secondary school? I don’t think US students remember that much of whatever we do teach there anyway.

[1]: https://www.google.com/books/edition/A_Concise_History_of_Ma... or https://archive.org/details/concisehistoryof0000dirk

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college_physicsJan 2023

Math always seemed a bit arbitrary to me. Why and how did all those fields and branches develop, why are some so much more intuitive than others etc. What helped me cope with that challenge (and ultimately be a better learner / user of mathematics) was digging into the history of mathematics. Many great books in that genre but a very influential one for me was the Concise History of Mathematics by Dirk Jan Struik

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hackuserOct 2016

Coincidentally, I am reading a leading history of mathematics, and just read the section on Mesopotamian math (the source of our base 60 customs, such as time, degrees in circle, etc.).

The Sumerians (of Mesopotamia, as was Babylon) not only used base 60, but also were the first known to use position or place value to indicate power of 60 the same way we do in base 10, a significant invention. For contrast, the Romans did not use position: IV is 4, not 15. Thus 11 (imagine Sumerian characters; sorry I don't know my Unicode well enough) in Sumerian is 61 in our contemporary system, and 563 in Sumerian would be 18,363 today. I'm impressed: Could people work with these numbers in their heads? Did someone doing Sumerian addition and multiplication have to memorize 60 x 60 tables, the way we memorized 10 x 10 tables in grade school? (The historian is silent on this matter.)

> if you point just the joints, not the tips, you get base 12. / If you count multiples of 12 with the five fingers in the other hand, you get to 60. / And this is the reason we have the 12-hour ...

The historian doesn't mention this (and how would anyone know today how the Mesopotamians counted on their hands?), but does say, "There is reason to believe that this choice of 60 rather than 10 as a unit occurred in an attempt to unify systems of measure, although the fact that 60 has many divisors may also have played a role."

Other societies commonly have used base 20 (my speculation: maybe natural if you are barefoot or wear sandals) and base 5. I highly recommend the book, the leader in its time (1987) and maybe still today:

A Concise History of Mathematics, 4th revised Ed., by Dirk Struik

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Arun2009Jul 2010

I am NOT a Mathematician, but FWIW, here are my antidotes to the crisis in meaning that you are facing:

1. You most likely wouldn't have had a problem solver's education. So the first thing to do would be do start understanding how problem solvers approach Mathematics. I suggest two books:

- The Art and Craft of Problem Solving by Paul Zeitz

- How to Solve It by George Polya

There are also others, e.g., http://www.amazon.com/Math-Olympiad-Resources/lm/1SWDJ5NA047...

Keep in mind that most proofs you see are highly polished for the sake of clear presentation. The route Mathematicians take to reach the proofs are almost always messy. And, unfortunately, they like to clear their tracks.

A great way to learn how to solve problems is to find a good problem solver and asking them to think out loud while they are solving problems. Also, try to find alternative proofs of any proof you learn.

2. Understand the history behind what you're studying. How did the ideas you're trying to learn (Abstract Algebra, Topology, Vector Analysis, etc.) come about? This will add an immense amount of meaning to your subjects.

I recommend the following books:

- "Men of Mathematics" by ET Bell. Also "The Development of Mathematics" by the same author.

- "A Concise History of Mathematics" by Dirk Struik,

- "A History of Mathematics" by Boyer

- And of course, the internet.

3. Read a few "big picture" books side-by-side. A few suggestions:

- "Foundations and Fundamental Concepts of Mathematics" by Howard Eves

- "Concepts of Modern Mathematics" by Ian Stewart

4. IMHO - and this is just my preference - study application of Mathematics to Physics and Engineering. Physics especially was an inspiration for a lot of Mathematics, and in addition, this will also let you solve concrete problems using the tools you learn.

5. During my undergraduate and graduate periods, I found several Schaum's and Dover books helpful. They're usually short and pretty cheap.

6. Initially, do not let rigor get in the way of understanding the content. Fourier, Newton, Euler, etc. weren't all that rigorous by modern standards.

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mindcrimeAug 2024

I've been going through that very video lecture series the last couple of weeks. Good stuff. And in the lectures he mentions a number of books. I looked a few up on Amazon, and then looked at the associated Amazon recommendations, and so far have this small list of books related to Maths history that look worth reading:

  Mathematics and Its History (Undergraduate Texts in Mathematics) 3rd ed. 2010 Edition by John Stillwell

  The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) by Carl B. Boyer

  A History of Mathematics by Carl B. Boyer

  A Concise History of Mathematics: Fourth Revised Edition (Dover Books on Mathematics)A Concise History of Mathematics: Fourth Revised Edition (Dover Books on Mathematics) by Dirk J. Struik

  Introduction to the Foundations of Mathematics: Second Edition (Dover Books on Mathematics) Second Edition by Raymond L. Wilder

  Mathematical Thought from Ancient to Modern Times by Morris Kline (3 volume set)

  The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time by Jason Socrates Bardi

There is also a "thing" in mathematics that is sometimes called the "genetic approach" where "genetic" is roughly equivalent to "historical" or maybe "developmental". IOW, a "genetic approach" book teaches a subject by tracing the development of the subject over its history. One popular book in this mold is:

  The Calculus: A Genetic Approach by Otto Toeplitz

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SomeoneFeb 2020

“A Concise History of Mathematics” by D.J. Struik apparently (I have read only a tiny part of it) is good, but being 70+ years old, it is getting more and more dated.

It also doesn’t discuss the mathematics itself in much depth; it more connects topics and has references (plenty of them) for those who want to learn about those topics.

“The World of Mathematics” by J.R. Newman isn’t a history, but more a sample of pure and, mostly, applied (“How to hunt a submarine” is the title of a chapter on operations research) mathematics.

I think it is worth mentioning, though, certainly for “tourists” who aren’t aiming for full coverage of the subject, but just want to visit nice viewpoints.

Also, I think it’s quite readable for non-mathematicians, as it doesn’t do much ‘real’ math (Stillwell's _Mathematics and its History_, mentioned elsewhere, has more of that in its first 25 pages than this 1000+ page work), and its chapters can be read in isolation.

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