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Mathematics for the Million: How to Master the Magic of Numbers
"It makes alive the contents of the elements of mathematics."―Albert Einstein Taking only the most elementary knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus. His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order―a language Hogben shows one can both master and enjoy.
656 pages, Paperback
First published March 1, 1937
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Displaying 1 - 25 of 25 reviews
June 20, 2017
This is one of the strangest maths books you are ever likely to encounter. Written in the 1930s and reissued in 2017, it's an attempt to provide mathematical instruction up to around A-level standard (though obviously the curriculum has changed a lot) for someone who, perhaps, doesn't respond well to the classroom and works better from self-teaching.
It's telling of the way popular science was considered in the period that apparently the author delayed publication as he was up for election to Fellowship of the Royal Society, which back then was dead against science popularisation.
Hogben, in a distinctive, mellifluous (if sometimes prolix) style, starts with the basics of arithmetic and leads us all the way through to calculus. Unlike his contemporaries, who were all for working through hundreds of geometry proofs for completeness, Hogben fills in the parts at each stage of mathematical development needed to reach the next stage and gives us no more.
The narrative here is very much centred on the application of mathematics through history. We see how geometry might have been used by Egyptian architects, and how trigonometry benefits those who need to navigate by the stars. The only problem with this learning-through-history approach is it can sometimes be hard to then relate what has been learned to uses in the present day.
Lancelot Hogben never intended this to be a fun read to pootle through just for the sake of it. The book is peppered with many exercises. It seems to be devised as a self-teach textbook of the future (as seen from the 1930s), throwing away the strictures of the rigid teaching approach of that period for something that is more approachable.
It's hard to say how well it delivers from the modern viewpoint of someone who has gone through all this stuff at school in a fairly traditional way. Clearly a lot of people decided it was a good approach back then: the book might not have made the 'million' in the title but certainly sold many copies.
To the modern eye, there is a danger of the book falling between two stools. It's not approachable enough to read purely for fun, but Hogben's distinctive, quirky style, combined with what is sometimes a rather tedious approach to the maths, means that it's not the best way for a modern reader, with no mathematical training, to learn about the subject. It stands best as a unique and fascinating oddity in the history of mathematical books for the general public - and as such is worth taking a look at.
It's telling of the way popular science was considered in the period that apparently the author delayed publication as he was up for election to Fellowship of the Royal Society, which back then was dead against science popularisation.
Hogben, in a distinctive, mellifluous (if sometimes prolix) style, starts with the basics of arithmetic and leads us all the way through to calculus. Unlike his contemporaries, who were all for working through hundreds of geometry proofs for completeness, Hogben fills in the parts at each stage of mathematical development needed to reach the next stage and gives us no more.
The narrative here is very much centred on the application of mathematics through history. We see how geometry might have been used by Egyptian architects, and how trigonometry benefits those who need to navigate by the stars. The only problem with this learning-through-history approach is it can sometimes be hard to then relate what has been learned to uses in the present day.
Lancelot Hogben never intended this to be a fun read to pootle through just for the sake of it. The book is peppered with many exercises. It seems to be devised as a self-teach textbook of the future (as seen from the 1930s), throwing away the strictures of the rigid teaching approach of that period for something that is more approachable.
It's hard to say how well it delivers from the modern viewpoint of someone who has gone through all this stuff at school in a fairly traditional way. Clearly a lot of people decided it was a good approach back then: the book might not have made the 'million' in the title but certainly sold many copies.
To the modern eye, there is a danger of the book falling between two stools. It's not approachable enough to read purely for fun, but Hogben's distinctive, quirky style, combined with what is sometimes a rather tedious approach to the maths, means that it's not the best way for a modern reader, with no mathematical training, to learn about the subject. It stands best as a unique and fascinating oddity in the history of mathematical books for the general public - and as such is worth taking a look at.
May 24, 2008
I read this in high school or shortly thereafter. I like the way the Author presents the concepts historically. Once I found a paperback version, I bought it immediately. As soon as my sister, an ex-math teacher, saw it, she wanted it, so I had to buy another for her. The projects would probably be good for parents to do with their kids, like the makeshift astrolabe. I would recommend this to homeschoolers and others who want to expand their knowledge of both mathematics and its history.
Currently reading
August 31, 2014Okay, a book on math that's over 600 pages long! Can I get through this?
Well, I've read over 600 pages of Charles Beaumont stories, so why not? Not that it will be easy to choke down this much math, but it's surely possible with a bit of discipline.
Hogben starts with an interesting story about how Diderot was shamed in a public debate with Euler, who presented a purported mathematical proof of the existence of God. Because Diderot had no knowledge of algebra, he conceded the debate and walked out. Weird, eh?
Hogben then explains how Achilles can catch up to the tortoise. He explains why this was such a puzzle to the Ancient Greeks, and how the puzzle can be elegantly and simply solved by present-day, grade-school mathematical expressions and a simple graphical diagram. This is weird, too! To think that the giants of Greek thought could be so stumped by such a simple problem for lack of simple tools and simple language that everyone takes for granted nowadays.
I was particularly intrigued by the following introductory comment:
"Our studies in mathematics are going to show us that whenever the culture of a people loses contact with the common life of mankind and becomes exclusively the plaything of the leisure class, it is becoming a priestcraft. It is destined to end, as does all priestcraft, in superstition."
Well, I've read over 600 pages of Charles Beaumont stories, so why not? Not that it will be easy to choke down this much math, but it's surely possible with a bit of discipline.
Hogben starts with an interesting story about how Diderot was shamed in a public debate with Euler, who presented a purported mathematical proof of the existence of God. Because Diderot had no knowledge of algebra, he conceded the debate and walked out. Weird, eh?
Hogben then explains how Achilles can catch up to the tortoise. He explains why this was such a puzzle to the Ancient Greeks, and how the puzzle can be elegantly and simply solved by present-day, grade-school mathematical expressions and a simple graphical diagram. This is weird, too! To think that the giants of Greek thought could be so stumped by such a simple problem for lack of simple tools and simple language that everyone takes for granted nowadays.
I was particularly intrigued by the following introductory comment:
"Our studies in mathematics are going to show us that whenever the culture of a people loses contact with the common life of mankind and becomes exclusively the plaything of the leisure class, it is becoming a priestcraft. It is destined to end, as does all priestcraft, in superstition."
March 2, 2007
I actually really enjoy this book but the first time this book was given to me I passed it on to a friend who is much more math loving and math inclined than I. A few years later I asked him how he enjoyed it and he proceeded to become my tutor. I don't know that I would have developed such a strong interest, respect and a certain fondness for a language that I would have sworn could never be a native tongue of mine.
This isn't an easy affair, though some readers out there are probably laughing and saying "I mastered the highest level of math covered in that book by the time I reached 8th grade." If so, more power to you, I applaud you.
This isn't an easy affair, though some readers out there are probably laughing and saying "I mastered the highest level of math covered in that book by the time I reached 8th grade." If so, more power to you, I applaud you.
February 13, 2013
Hard for me to believe that anyone would rate this book lower than a five. It is a unique and fascinating book that looks at the historical development of mathematics with a clear focus on the most practical of mathematical applications (from geometry to statistics) but doesn't shy away from the great leaps of logic and calculus. It is not at all a classic textbook - but is far better. I learned more math from this book as a young teen than from any other source or teacher - and I LIKED learning it.
It's written in a pretty old-fashioned style nowadays but that plus the beautiful hand drawn diagrams make it a fantastic book
It's written in a pretty old-fashioned style nowadays but that plus the beautiful hand drawn diagrams make it a fantastic book
March 24, 2008
I keep this around as a basic text. It covers everything you need to know about mathematics. Lancelot Hogben is 007. His person history is wild.
Read
February 21, 2010One of my favorites . Book to be studied over and over again !
long-term-reading
March 17, 2016When I think of this book, I think of my father who died 23 years ago . He had a copy of this book given to him by his father-in-law.
This was either to get him through U-Conn Engineering Math after WWII or artillery school-Officer training during WWII. He was very good at practical mathematics and could estimate distances by sight as well as figure out math in his head which was helpful for his as a textile mill manager.
I am puttering around with this one and am reminded of him.
This was either to get him through U-Conn Engineering Math after WWII or artillery school-Officer training during WWII. He was very good at practical mathematics and could estimate distances by sight as well as figure out math in his head which was helpful for his as a textile mill manager.
I am puttering around with this one and am reminded of him.
Want to read
August 27, 2008I think it will take me a year to finish this book. I have to stop to think about most of the pages and even go to the dictionary and look up some of the words. I will eventually finish. I like the way that the author tells the history of mathematics and its uses starting from ancient times. I still don't fully understand some of the concepts, so I'll probably read it again someday.
March 31, 2011
great book . Essential for anybody who wants to understand mathematics
February 10, 2021
Does exactly what it says on the box: takes the reader through the history of mathematics while giving examples and questions so the reader can apply what they’ve learned in each chapter; which is perfect if you’re looking to refresh your maths understanding or upgrade it.
I’m not going to pretend I now understand calculus but at least I’m in the same ballpark which is an achievement
Only negative comment would be that the statistics chapter could’ve been better since it’s not totally clear when exactly to use specific formulas.
I’m not going to pretend I now understand calculus but at least I’m in the same ballpark which is an achievement
Only negative comment would be that the statistics chapter could’ve been better since it’s not totally clear when exactly to use specific formulas.
January 29, 2009
Math for the layman, written in 1940's. (Quotes on back from Einstein and H.G. Wells.) Excellent writing, though a bit dated in areas. Possibly because it's so dated, had some interesting angles on some concepts. Probably not for someone who wasn't already comfortable with some math.
(Really 4.5)
(Really 4.5)
October 12, 2016
must read for all those who find mathematics challenging.
September 18, 2021
I don't want to mark this as 'read' as this book is something I keep on the shelf to constantly refer back to. Lancelot even says at the beginning that the best way to read this book is to skim it once to get the basic concepts, then read it again to appreciate it. Don't expect to understand everything the very first time. These topics all take practice.
Every educator should be required to read this or something like it. The art of making mathematics fun and interesting has been losing ground in the current school curriculum in lieu of rote repetition, homework and quizzes. Every time my students are ready to move to a new topic, I refer to this and always find a realistic and interesting approach to the topic using real-life examples and fun stories.
Every educator should be required to read this or something like it. The art of making mathematics fun and interesting has been losing ground in the current school curriculum in lieu of rote repetition, homework and quizzes. Every time my students are ready to move to a new topic, I refer to this and always find a realistic and interesting approach to the topic using real-life examples and fun stories.
Read
February 6, 2020George Orwell once used a sample of this author's work as an example of bad writing. I think the problem with this book is not in the grammatical style (which by today's standards isn't that bad), but in the historical approach used to describe complicated mathematical ideas. He begins dealing with spherical trigonometry in the very first chapter, which I don't think anyone would mistake for entry-level math. I eventually gave up halfway through the book, intending to come back to it after I picked up more math elsewhere, but I'm getting a bit old to make that happen. Soooooo many books out there....
September 22, 2024
Some fascinating insights into the history and various uses of mathematics, but I for one found it heavy going. I was daunted by pages of formulae or long paragraphs of explanations in words. It has beautiful illustrations which do help.
February 19, 2022
Absolutely brilliant
February 28, 2008
Noam Chomsky cites the author of this book as a "left intellectual" because he tries to popularize mathematics.
In the introduction he writes some pretty powerful words about what mathematics is and what it does...
the meat of the book (which i haven't read yet, and may not get around to reading any time soon) is a historical telling (mostly, but not exclusively, from the 'western' perspective) of how several mathematical ideas developed and the way in which they were used at the time.
However, the introduction itself is worth checking out!
In the introduction he writes some pretty powerful words about what mathematics is and what it does...
the meat of the book (which i haven't read yet, and may not get around to reading any time soon) is a historical telling (mostly, but not exclusively, from the 'western' perspective) of how several mathematical ideas developed and the way in which they were used at the time.
However, the introduction itself is worth checking out!
May 25, 2014
Surprisingly good for a lefty discussion of relatively easy maths.
The parts where Hogben teaches us about how numbers work are wonderful examples of math instruction; the parts where he waxes lyrical about socialism could well lead to a wonderful example of mass destruction.
The parts where Hogben teaches us about how numbers work are wonderful examples of math instruction; the parts where he waxes lyrical about socialism could well lead to a wonderful example of mass destruction.
May 6, 2015
Decent math, dry exposition, intrusive politics.
George Orwell quotes Hogben among others in his essay Politics and the English Language as examples of writing "below the average" that exhibit "staleness of imagery" and "lack of precision". Fitting.
George Orwell quotes Hogben among others in his essay Politics and the English Language as examples of writing "below the average" that exhibit "staleness of imagery" and "lack of precision". Fitting.
gave-up-on
March 13, 2012I'm actually reading the second edition, from 1937, the 17th printing (1945). It has 686 pages.
May 10, 2015
greta book
January 21, 2016
Grade: 78% / 'C'
August 6, 2015
A sweep of some grandeur over the rise of mathematics, from calendar civilisations to the great flowering in Alexandria and beyond. A breathtaking achievement.
Read
February 11, 2018I wanted to be the person this book is written for, but am not. DNF at 100 pages.
Displaying 1 - 25 of 25 reviews