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stephenmeansme's review against another edition
2.0
Milo Beckman set out to show the reading public what real math is, without using numbers. Did he succeed? In some sense, I'm an unreliable reviewer, because I have a university degree in mathematics, so I already have an idea of what real math is. I know very well what Beckman means when he says that at some point, mathematicians stop worrying about or even using "numbers" (that is, quantities represented in Arabic numerals): it's both a joke and also a fact that real mathematicians hate doing arithmetic with numbers greater than, say, 10. And I appreciate the goal of trying to get this across using words and pictures rather than lots of scary notation.
The book is divided into sections for broad areas of the real-mathematics landscape: Topology, Analysis, Algebra, Foundations, and Modeling. Except for Foundations, each section has a few sub-sections. Most of the good stuff is in the first few sections, IMO: Beckman does a nice job of explaining topology's focus on "shape" and leading that into the example of classifying manifolds; he also sketches some good intuition about how the continuum (real line) is used in calculus. The Algebra section starts to suffer from disunity, but the first part about abstraction was pretty good. Modeling has its moments, but no cohesion.
My problems with the book are twofold, possibly describable as "choice of audience" and "choice of mathematics."
First, I started to become unsure who Beckman's target audience was. The selection of mathematics (see below) may or may not be interesting to a high school student, but sufficiently-interested students would probably want a meatier book anyway. He often affects a certain "mystery box" presentation ("There's X, but I can't tell you about X yet") that I found distracting and potentially condescending. It was mildly mysterious.
Second, the choice of what mathematics to present was a bit odd. While the continuum bits of the Analysis section were good, the section overall seemed a bit too trivia-oriented (types of infinities!); similarly with Algebra and Foundations. If the task had fallen to me, I might have gone for more of a themes or tools approach: linearity, invariance, and classification, for example, are three themes that show up across a wide range of mathematical topics. On the tools side, there might be simulation (including probabilistic methods!), induction, and abstraction, these last two being in the book already. These cross-threads could give the book a better sense of unity, and properly conveyed, could give close readers a sense of accomplishment for spotting the connections early.
As a minor point, the Foundations section seemed the most gratuitous, mostly because most "real" mathematicians don't care about foundations, but also because it's structured as a Hofstadterian dialog about the nature of mathematical truth. It spends some pages on a back-and-forth about the history of mathematics as a knowledge enterprise and its association for a few centuries with European imperialism. I'm not going to freak out like some other reviews and say "warrgarble wokeism," but to bring it up, only as shallowly as it was done here, seems more like flag-waving than enlightening or educating. (The other payoff is passing mention of Goedel's theorems, for which GOEDEL, ESCHER, BACH exists but also is something I think is better left to experts.) The Modeling section features other odd digressions, as when Beckman speculates about physics being like an automata (other examples: Conway's "game of life"), which is either naive-realist or Tegmarkian and I don't like either option. Science can use math as a description language but science isn't math!
2.5 stars rounded down. Nice try?
The book is divided into sections for broad areas of the real-mathematics landscape: Topology, Analysis, Algebra, Foundations, and Modeling. Except for Foundations, each section has a few sub-sections. Most of the good stuff is in the first few sections, IMO: Beckman does a nice job of explaining topology's focus on "shape" and leading that into the example of classifying manifolds; he also sketches some good intuition about how the continuum (real line) is used in calculus. The Algebra section starts to suffer from disunity, but the first part about abstraction was pretty good. Modeling has its moments, but no cohesion.
My problems with the book are twofold, possibly describable as "choice of audience" and "choice of mathematics."
First, I started to become unsure who Beckman's target audience was. The selection of mathematics (see below) may or may not be interesting to a high school student, but sufficiently-interested students would probably want a meatier book anyway. He often affects a certain "mystery box" presentation ("There's X, but I can't tell you about X yet") that I found distracting and potentially condescending. It was mildly mysterious.
Second, the choice of what mathematics to present was a bit odd. While the continuum bits of the Analysis section were good, the section overall seemed a bit too trivia-oriented (types of infinities!); similarly with Algebra and Foundations. If the task had fallen to me, I might have gone for more of a themes or tools approach: linearity, invariance, and classification, for example, are three themes that show up across a wide range of mathematical topics. On the tools side, there might be simulation (including probabilistic methods!), induction, and abstraction, these last two being in the book already. These cross-threads could give the book a better sense of unity, and properly conveyed, could give close readers a sense of accomplishment for spotting the connections early.
As a minor point, the Foundations section seemed the most gratuitous, mostly because most "real" mathematicians don't care about foundations, but also because it's structured as a Hofstadterian dialog about the nature of mathematical truth. It spends some pages on a back-and-forth about the history of mathematics as a knowledge enterprise and its association for a few centuries with European imperialism. I'm not going to freak out like some other reviews and say "warrgarble wokeism," but to bring it up, only as shallowly as it was done here, seems more like flag-waving than enlightening or educating. (The other payoff is passing mention of Goedel's theorems, for which GOEDEL, ESCHER, BACH exists but also is something I think is better left to experts.) The Modeling section features other odd digressions, as when Beckman speculates about physics being like an automata (other examples: Conway's "game of life"), which is either naive-realist or Tegmarkian and I don't like either option. Science can use math as a description language but science isn't math!
2.5 stars rounded down. Nice try?
ramakrishnanpooja's review against another edition
5.0
Really extraordinary. If only Milo had been my professor, my life would’ve looked so different!
whyhisbald's review against another edition
4.0
I cannot believe this dude got me to read a proof and I enjoyed it (?)
mcnan's review against another edition
5.0
WOW.
This book is so accessible, taking complicated subjects and translating them lovingly into digestible portions. I have always been enamored by math and numbers, but intimidated to approach the art of M A T H E M A T I C S, seeing it as a whole new language only for those with lots of training and prestige. I will be referring back to this book when I feel overwhelmed in math, especially with modelling. I loved the chapter on algebra, it was really eye-opening.
The illustrations were charming and helped visualize some of the concepts.
I did see one or two numbers in this book though, spelling them out still counts!
This book is so accessible, taking complicated subjects and translating them lovingly into digestible portions. I have always been enamored by math and numbers, but intimidated to approach the art of M A T H E M A T I C S, seeing it as a whole new language only for those with lots of training and prestige. I will be referring back to this book when I feel overwhelmed in math, especially with modelling. I loved the chapter on algebra, it was really eye-opening.
The illustrations were charming and helped visualize some of the concepts.
I did see one or two numbers in this book though, spelling them out still counts!
clintonwatton's review
informative
lighthearted
reflective
medium-paced
5.0
Among all of the math books I have read, few present the more advance and abstract areas of the subject in such a playful and accessible way. Milo tackles ideas of topology, shape, dimension, automata, etc. in a manner that is not overwhelming yet sparks curiosity. As a math teacher and someone who holds a graduate degree in mathematics, I highly recommend this book to anyone that may have a mind for exploring different ways of thinking and to learn about a less dull side of mathematics that is rarely seen in traditional classrooms.
thejoyofbooking's review against another edition
5.0
I adored this book. It's true to its premise - no numbers, but mind-blowing mathematical ways about thinking about everything in the entire universe (literally). I was even more shocked when I read the author's bio and realized how young he is. The tone is so inviting and mature, I expected the book to be written by a long-time college professor or something, someone who had learned how to introduce people to a complex topic. Perhpas it's unfair that the author's youth makes the tone so much more impressive to me, but it's true. This will be on my recommended and re-read lists for sure.