Thursday, March 09, 2017


Logicomix is the story of the logician Bertrand Russell, as told by the man himself, as told by Apostolos Doxiadis and Christos H. Papadimitriou, drawn by Alecos Papadatos and Annie Di Donna. It is not a book about logic, or the history of logic, or how to live your life in the most logical manner. It really is a story about a real person, and I think it's really well done. For real.

The story follows Bertrand Russell from when he was a very small boy, and was still learning about how to see the world around him. Russell learns of the beauty and elegance in proofs, and sets off to try and prove all the things! This is the meat of the book, and it reads as thrilling a story as any.

This story is told via flashback, as Russell gives a talk to agitated peace protestors during World War II. This, in addition to letting Russell narrate, gives more direction to the story as a whole.

But Logicomix is not just that story. It also tells a part of the story of how Logicomix came to be, showing the day when Christos comes on board to help. Russell's story is presented with the authors and artists talking about what to include in the story. The whole layered narrative thing is fun, partly because so many people can interject, which colors the story just that little bit more. It is very well done.

So, if you think a story about searching for truth told through layered narratives sounds cool, then you should read Logicomix. And also I guess if you like logic or whatever. Or if you're curious about what logic even is, but don't want to actually do any of the hard stuff. Then this is a good book for you. Yep, I am happy with this paragraph's construction.

Wednesday, March 01, 2017

The Mathematics of Various Entertaining Subjects

The Mathematics of Various Entertaining Subjects, edited by Jennifer Beineke and Jason Rosenhouse and written by a whole bunch of people, does not have an interesting title. I'd guess that, for the vast majority of people, the book is just as boring as it sounds. However, for math nerds like me, it's really interesting, and a fun introduction to how math is done in "the real world."

The Mathematics of Various Entertaining Subjects is a collection of 17 chapters, each written by different folks, and each about the some sort of game or puzzle. All of them (except maybe the first two) are heavy in mathematical language and notation. Some chapters explain the background really well, others not so much. I straight-up skipped a few of the chapters. The ones that I did read were, for the most part, very interesting. There's a lot of variety to the subjects of the chapters. One might go so far as to say that there are various entertaining subjects.

That's about as much as I can say without going into the individual subjects in depth. So, let's look at one of the subjects. I present to you the heart of my favorite chapter, lucky 13, by Maureen T. Carroll and Steven T. Dougherty. It's about tic-tac-toe on what are called "affine planes." The smallest interesting affine plane is this:
Tic-tac-toe is played on this plane the same way as on a normal one, but on this plane there are four extra lines (the big curvy ones). This looks complicated, but all that happens to tic-tac-toe is that four more winning arrangements are added:
These new four are the last ones on the bottom, and they make a sort of diagonal T-shape. Try getting together with a friend and seeing what this changes. I spent an entire period of Physics class messing with these, and had more fun than was probably warranted.

So, if you think you want to see some fancy math, most of which isn't presented for beginners, then read The Mathematics of Various Entertaining Subjects. If you don't, then don't. If you're not sure, then start with a friendlier math book. I've got a lot of them in the "numbers" tag now.

Have a good day and a great life. Peace!

Wednesday, February 22, 2017


Zero is about nothing. By which I mean, it's about the idea of a void, a lack-of-thing, as being a sort of thing itself. It's written by Charles Seife, who also wrote Proofiness. Zero is similar to A Brief History of Infinity, by Brian Clegg, in that it's more of a history book than it is a math or science book. They're also similar because they talk about infinity, because zero is "infinity's twin."

The first six chapters of Zero (or the first seven, depending on how you count them) are about the idea of nothing slowly working its way into the mainstream, followed closely by the idea of the infinite. There was actually a lot of resistance to both of these ideas, especially in the West, which is made even more interesting by Seife's flowery writing. I'm not entirely sure what "flowery writing" actually means, but I'm pretty sure it happens in this book. Zero does technically go into some math, but never in much detail. There's just enough math to make sense of all the pretty pictures.

The last three chapters are about zero in physics, where it likes to cause problems. This second part seems much weaker than the first part; Seife uses quite a bit of hand-waving, and never shows us a single equation. I think that if Seife would show us the actual equations and where the zeros are, we would better understand why zero is to blame for these quirks. That said, I'm sure some people will be glad that the math all but disappears when the physics comes on.

If you wonder how ideas take hold, or like history, or are somewhat confused about zero yourself, then maybe give Zero a try. For what it's worth, I finished it in just three days, so it can't be all that boring. (Although, that probably says more about my schedule than it does about the book.) I think the best way to understand what Zero is like is probably just to read the introduction (which Seife calls "Chapter 0"), so I've just typed it up here. This might be illegal. Don't tell anyone. The point is, he remains that flowery throughout the book, and if you like that section, I think you can enjoy the rest.

Sunday, February 19, 2017


Flatterland is full of puns and science. Really, if it weren't for the name "Ian Stewart" on the front, I'd suspect it had somehow been written by me. Flatterland is a "sequel" of sorts to Edwin A. Abbott's Flatland, which I suppose you should technically read first, although I think Flatterland stands perfectly well on its own. Still, a quick review/summary of Flatland is in order.

Boop. Just did a quick review. Two paragraphs. It doesn't even have a picture of the cover. Go read it, if you'd like.

Anyways, back to Flatterland. As the tagline says, it's like Flatland, only more so. And with a healthy helping of Alice in Wonderland to boot. Flatterland is set about a hundred years after Flatland, and follows the adventures of Victoria "Vikki" Line, a woman who finds her some-number-of-greats-grandfather's book, which is entitled Flatland. (Yes, they are actually the same book.) Anyways, Vikki reads Flatland, and in it finds instructions for summoning a being from Spaceland, in a way that is kind of hilarious.

So, Vikki summons someone from Spaceland. However, she gets a bit more than she bargained for. Instead of the stuffy, boring old Sphere from Flatland, she meets a loud, energetic, grinning creature known as the Space Hopper, who can travel through much more than just stuffy, boring old Spaceland. The Space Hopper equips Vikki with a Virtual Unreality Engine, or VUE, and takes her on a tour of all sorts of spaces and geometries, meeting many strange people along the way. They pay special attention to a strange place called Planiturth, and the fact that its inhabitants don't really know which space they're in.

Personally, I really liked Flatterland. I'm a big fan of puns, and math, and paradoxes, and big toothy grins, and winks directed at the fourth wall, so what's not to like? I think Ian does a good job of describing and explaining all the spaces, and why they're all cool. If I had one complaint, it would be that there aren't enough pictures. Actually, I do have that complaint. A book about geometries should have more pictures in it. But, besides that, it's a fun read, and it stays crazy enough to always keep you guessing. If you like bending your brain a bit, and you don't mind a good pun every once in a while (or a bad pun (or twenty)), then I think you should try Ian Stewart's Flatterland.


Flatland, by Edwin A. Abbott, is a memoir written by one A. Square, who inhabits the two-dimensional universe known to us as Flatland. The first half of the book is about Flatland itself, and the lives of the people inside it, who live in a strictly ordered society where social class is determined by the number of sides you have. Women, all of which are lines, have the lowest status (even though they are technically really thin quadrilaterals). There's also this freaky thing where kids are beaten into being more regular, and color is not allowed, and it's kind of terrible.

The second half of the book is about A. Square's experience of being visited by a Sphere from Spaceland, which has a third spatial dimension. As A tries to wrap his head around the fact that there can be a third dimension, the reader gets to try to thing about what a fourth dimension could mean. The Sphere also takes A through the first and "zeroth" dimensions, which is fun. Then the Sphere takes A back home, at which point A is promptly thrown in jail for being a lunatic. If you like dystopias and/or thinking about higher dimensions, then Flatland is a book you might like.

Friday, February 10, 2017

Our Mathematical Universe

Our Mathematical Universe is about big questions: Why are we here? What made it all? What's it all made of? Where did we come from? Where will we go? Where did we come from, Cotton Eye Joe? and so forth. More specifically, it is about Max Tegmark's answer to all those questions.

Tegmark takes us on a tour of the extremes of physics, from the epic scales of our entire universe to the smallest scales of atoms and space. The part about cosmology and the beginning of the universe is especially good, because Tegmark has personally worked with the data from satellites investigating the Cosmic Microwave Background Radiation. He also talks about the possibility of multiverses, and identifies four different "levels" of multiverse. I like that he stresses that there is no such thing as a "multiverse theory" in physics; multiverses are not a theory, but a prediction of other theories.

Then he talks about his idea that, in the end, the entire universe is a mathematical object. He makes quite the compelling case for the idea, essentially arguing that for physics to mean anything it has to be true, but in the end he didn't convince me. It's kind of a nice idea, though. A good effort. Anyways, if you'd like to see the structure of the entire book, it's something like this:
Yep. That's taken right out of the book. Tegmark did some of my job for me. Nice of him.

When Tegmark says "my quest for the ultimate nature of reality," he means it. The book is about his quest. Our Mathematical Universe could equally accurately be called Max Tegmark is a Nerd, although I doubt that would sell quite as well. The book is filled with personal anecdotes and little asides, which I think adds to it a lot. Then, of course, there's the whole "reality is math" thing that he believes. Still, he's an interesting person with interesting ideas, so it's fun to go on the "quest" with him. He certainly kept me to the end, at least. If you're also interested in the big questions about what it's all about, and you don't mind having a friend along for the ride, then you would enjoy reading Our Mathematical Universe.

Friday, January 20, 2017

What's Math Got Do Do With It?

Jo Boaler's What's Math Got To Do With It? is about math education. It might surprise you to know that I am interested in this subject. Then again, it might not. I think the best audience for this book is mostly people like me, who are interested in teaching, and maybe parents who want to help their kids learn math.

In other words, What's Math Got To Do With It? is exactly what it says on the cover: it's a book about how teachers and parents can transform mathematics learning and inspire success. It mostly focuses on math teaching in the U.S. and the U.K. and it presents actual research studies on what works and what doesn't. It is well-written and clear, and gives strategies with concrete examples.

In conclusion, if you are a how teacher or parent who wants to transform mathematics learning and inspire success, then you should read What's Math Got To Do With It?.

Sunday, January 08, 2017

Prime Obsession

Prime Obsession is written by John Derbyshire, who also wrote Unknown Quantity. Like Unknown Quantity, it is a book about the history of math. Specifically, it's about the Riemann Hypothesis, how it came to be, and what it actually means.

The Riemann Hypothesis is the greatest unsolved problem in mathematics, at least according to the subtitle. It makes a statement about a function (which is described in the book) that has a deep connection with the prime numbers (which is also explained in the book). If you're the kind of person who reads math books, then you've likely already heard of the Riemann Hypothesis. It's one of the six remaining unsolved Millennium Prize puzzles, so proving it to be true or false will make you a million dollars richer.

Prime Obsession is divided into two parts. The odd-numbered chapters are math-heavy, and the even-numbered chapters focus more on history. This is done so that a reader who's just into math can only read the odds, and a reader who's just into history can only read the evens. I don't really like this split; I preferred the structure in Unknown Quantity, where both areas were present throughout the entire book. The split between the chapters removes the interesting math from the interesting stories of the mathematicians. As a more math-leaning person, I found the even chapters a bit slow. Because the people and their stories were not connected with their ideas, a lot of the people become forgettable to me.

All in all, though, I did like the book. Derbyshire explains everything clearly and takes time to ensure that the reader understands what's going on. This is the first source I've found which explains the zeta function's connection to the primes in a way that's clear and satisfying (although it does take a while to get there). I also like that, when Derbyshire does skip a few steps in the math, he takes a moment to explain that and why he is doing so. If you're curious about what this whole "Riemann zeta" business is about, then Prime Obsession is the book to read.

P.S.: You should also watch this video by 3Blue1Brown, which is about visualizing the zeta function. You can consider it a supplement to chapter 13, or you can just watch it because it's pretty.

Thursday, January 05, 2017

Elliptic Tales

You will probably not enjoy Elliptic Tales, by Avner Ash and Robert Gross. I enjoyed it a lot, but I suspect I’m in the minority on that. You see, Elliptic Tales is by far the most math-intense math book I’ve read. In my opinion, this is a good thing. However, the whole thing might be a bit… daunting to someone who is not actually into math.

Let me back up a bit. What is Elliptic Tales about? Well, Elliptic Tales is a book which will explain to you what exactly the Conjecture of Birch and Swinnerton-Dyer (or BSD Conjecture for short) is. This might be of interest because the BSD Conjecture is one of the six remaining unsolved Millennium Prize puzzles, meaning there is a reward of one million dollars for whoever proves it. To me it's of interest because I'm a nerd, and I want to know what kinda stuff is being worked on in math right now.

The thing is that the BSD Conjecture involves a lot of preparation, and although Ash and Gross do a wonderful job at explaining things, there are some patches in which everything is confusing for a bit. My advice for these parts is to just read on for a bit. Sometimes, Ash and Gross mention concepts that they don't actually introduce until the next paragraph, or even later than that. Trust me when I say that it mostly makes sense in the end. Also, use the glossary. It helps.

I think my favorite parts of Elliptic Tales are the ones in which they are teaching about something else. This is the first source I've found which explains projective geometry well, and some of the earlier stuff with generating series is cool enough to create a formula out of. They say you can skip Part 1, which deals with the degree of a polynomial, but I had a lot of fun reading it. Also, they reference that part later in the book, so if you haven't read it you feel a bit cheated and left out. How do I know how this feels, given that I did read Part 1? Because they also reference their previous book, Fearless Symmetry, and that's how it makes me feel.

So, I really enjoyed the book, because it taught me a lot. However, I realize that this isn't that big a selling point for most people. If you don't really like math, then stay away from Elliptic Tales, and instead read Things to Make and Do in the Fourth Dimension. If you do really like math, and are excited about learning math, then read Fearless Symmetry, so that you can later fully enjoy Elliptic Tales. And never, under any circumstances, read Bridges to Infinity. I think that about covers everything. Until next time!

Tuesday, January 03, 2017

Romeo and/or Juliet

Romeo and/or Juliet is a choose-your-own-adventure book by Ryan North. It has not only one, but several plots, as is typical of a choose-your-own-adventure book. Because of this, I can't really do a plot-focused review, and so I have been putting this off for like two months, because I don't really know what to say.

Romeo and/or Juliet is funny. It makes fun of the original Shakespeare work, pointing out the silly parts of the story and usually replacing them with even sillier ones. The narrator is more of a character than most of the characters, and likes to make anachronistic remarks. When reading, I pictured the narrator as a flying red fairy. You can also do this, if you want.

Well, that's all I've got. Next time, remind me to review a book with a stationary topic. If you like dumb laughs and/or Shakespeare, then you should read this book. Or, I guess I mean you should play it. Interact with it. Read sections of it, and then at the end of those sections make a decision between the offered choices and turn to the appropriate section, and then repeat this process until you get an ending.

See, this is why I had trouble.