Pretty darn funny, and accurate, depictions of Eastern European culture and academic math culture. Mixed with moving reminiscences about survival in WPretty darn funny, and accurate, depictions of Eastern European culture and academic math culture. Mixed with moving reminiscences about survival in WW2 on the Russian front.
Now, I really hate some of the awful parts of math culture: participants can only be either brilliant or mediocre, and there's absolute refusal to respect anyone who's not on the brilliant side... The book depicted these flaws well too, though it glorified them a bit too much for me.
It has very funny moments, but it's more subdued than the screwball comedy I expected from the synopsis on my copy's cover. It is *not* a zany chase full of people prying up floorboards during a funeral.
It's definitely clear out that the author is a scholar of the atmospheric sciences. The weather descriptions are never "It snowed and stayed cold," but rather "The high-pressure Arctic air mass had decided to stagnate."
The narrator's griping about Americans was spot on the first few times, & sounds just like some of my relatives---but it got old and repetitive. Did he start writing the same content in several chapters, then forget to edit it out?
Also, why does he spend almost no time (view spoiler)[talking to his newfound daughter and granddaughter? Of course it's hard for me to imagine the grief I'd feel at a parent's funeral, plus the narrator has all these other people's antics to deal with---but still, if my long-lost child wandered into my life, I'd forget all the rest and want to get to know them. Right (hide spoiler)]?
Favorite parts: * p.42: Dear reader, don't panic. Newton was barely past twenty when he invented calculus. It's pure adolescent whimsy at work. Think of the language of mathematics as shorthand that has been around for centuries, the equivalent of teenage texting, but for geeks. Yes, I know you don't know half the text abbreviations that your teenage children use, but you can figure out their argot if pressed, can you not? You can figure out this one as well. * p.91: "You spend too much time worrying about men, Anna. They are all alike. Pretty boring, really. Just pick one and keep him." * p.105: At the time I thought I had learned an obvious lesson. Do not fall in love with someone when that love is heavily dependent on the goodwill and kindness of your parents. Find someone else. It's a stupid thing to expect a family to help you tie up your love life into a nice bow, and smart people do stupid things far more often than most people realize. Now, looking back, I don't think that's the lesson that I should have learned. I should have understood that when you love someone, and they are being subjected to cruelty, you need to do whatever you can to shield them, to defend them, even if the source of that cruelty, maybe especially if the source of that cruelty, is your own mother. This is your obligation. There are no exceptions. * p.150: I knew the type. They had begun to invade Tuscaloosa, these young professors. Male and female, they were all so skinny, fit, and earnest, and so remarkably free of anxiety. When you asked them what they liked to do, they had two answers, their work and running. They ran an ungodly number of miles every week not to avert a health crisis, but simply because they loved to run. Who understood them? Endorphins saturated their blood, mixed with the caffeine from their no-fat lattes. A new generation had arrived, and it quite frankly was superior, if much more boring, than my own. * p.267: She had also started to develop the ability (or liability) of being in one place physically but only partially there mentally. It was like dealing with a cell phone wavering between one and two bars of reception, functional but a bit worrisome. Her mind was not in the here and now but was usually preoccupied... This habit of only sort of being present can drive nonacademics crazy. But it's the only way I know that anyone can solve intellectually difficult problems. It's a constant processing of ideas and techniques in the background that happens even when you dream. * p.276: "You think you've been lucky?" "I don't allow myself to be unlucky." * p.285: "It's the best place in the world for a smart man to be. All this money, all this opportunity, and only stupid, lazy Americans to compete against. It's heaven on earth."["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>["br"]>...more
So far, it's a great exposition of the things I love about math, at (what seems to be) a very relatable level for people who don't love math.
The styleSo far, it's a great exposition of the things I love about math, at (what seems to be) a very relatable level for people who don't love math.
The style is a bit choppy, often jumping from one metaphor to another without smooth transitions, but still it's an easy and pleasant read. The metaphors themselves (for math or its concepts) are excellent, and I will steal some next time I teach :)
p.27: "if you try and use complicated math for a situation that doesn't call for it, you'll think the math is pointless. It's a bit like using the Dewey decimal system if you only own twenty books."
The book reminds me of the great math teacher blogs out there (such as Dan Meyer's), with a welcoming and thoughtful approach. It's nice to see high school teachers in the trenches sharing this perspective with a VERY abstract & academic pure mathematician.
Second half is a fun, simple introduction to category theory. I knew nothing about it before, and I'm still not fully clear but at least I have some intuition now. Many of the examples are from group theory / abstract algebra -- perhaps because it sounds like category theory grew out of studying groups.
Nice examples of various kinds of proof, and the links / distinctions between knowledge, belief, and understanding. She gives the reader two different proofs and then asks, "Which of these two arguments did you find easier to follow? Which was more satisfying?" (p.258)
Or she illustrates how sometimes, "the mathematical proof is often not something that will convince you why it is true. Instead, it might convince you that it is true. ... Proof has a sociological role; illumination has a personal role. Proof is what convinces society; illumination is what convinces us." (p.274)
This helps me feel better about all the dense, technical proofs I have to read for my PhD. Why can't they just give intuitive reasons? Not merely because intuitive reasons are hard to create, says Cheng, but also because (p.277) "Proof is the best medium for communicating my argument to X in a way that will not be in danger of ambiguity, misunderstanding, or distortion" ... even though "When I read someone else's math, I always hope that the author will have included a reason and not just a proof" :)
And indeed, if you're a young student in math class being asked to jump through un-illuminating hoops, it's easy to get jaded and see math as a bunch of arbitrary right-or-wrong rules to memorize, instead of a tool for understanding the world.
Throughout the book, she writes with great respect for (and encouragement towards) readers who felt unhappy with their math education and grew to hate it. She breaks down the myths about what math is, what it's for, and what success means in math -- myths that are unfortunately still perpetuated in many schools today.
p.277: "many people grew up feeling great antipathy towards math, probably because of how they were taught it at school, as a set of facts you're supposed to believe, and a set of rules you have to follow. You're not supposed to ask why, and when you're wrong you're wrong, end of story. The important stage in between the belief and the rules has been omitted: the illuminating reasons. An illuminated approach is much less baffling, much less autocratic, and much less frightening."
I'll admit that some of the food examples riled me a bit -- too much talk about losing weight, and too much patience with ridiculous fad diets. If your book is about breaking down a bad stereotype (of math), it shouldn't reinforce other bad stereotypes/obsessions.
But if you can stomach (*rimshot*) those parts, it's a worthwhile book with a nice vision of how math education ought to go and what it means to be a mathematician....more
Sounds like a collection of papers and articles by the original historical developers or discoverers of various bits of math? Nice idea -- "read the mSounds like a collection of papers and articles by the original historical developers or discoverers of various bits of math? Nice idea -- "read the masters, not their students" as they say, which would be easier if they made collections like these easier to find!...more