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Mathematics: A Very Short Introduction (2002)

Tekijä: Timothy Gowers

JäseniäKirja-arvostelujaSuosituimmuussijaKeskimääräinen arvioMaininnat
739730,496 (3.62)2
The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?")… (lisätietoja)
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Näyttää 1-5 (yhteensä 7) (seuraava | näytä kaikki)
Math as a way of life, as a job, a hobby, as a foundation for civilization. ( )
  mykl-s | Aug 9, 2023 |
I know too much math to get much out of this. On the other hand, it's nice to get a refresher overview of the subject.
I may look at buying a few more "Very Short Introduction" books. ( )
  scottkirkwood | Dec 4, 2018 |
Nog te bekijken
  erikboekenwurm | Oct 31, 2018 |
A quick and easy read. Gowers manages to navigate the complex math well enough to provide the core insights of the topics without getting bogged down in technical details that trip up less mathematically savy readers. But it never feels like he is glossing over too much material either. This makes a nice supplement to other nontechnical introductory texts on math. ( )
  austin.sears | Feb 24, 2014 |
I got this book because I wanted to try to diversify my interests a bit, or, at least, soften my long-standing dislike of mathematics. It did that much, and it also showed me that math can be very much its own thing, and not just an unequal partner in "math & science"...numbers can be more than just a crutch for scientists to lean on so they don't have to learn how to talk properly.... (Ok, Gowers doesn't talk like that...but I do.)

(Tangent: I've tried reading some 'science' books, but they always seem to end up being about the man of science himself and his ego, and I really couldn't care less...they just don't seem to understand when they're selling their own loser philosophy, and I don't want it, and when they can't string two sentences together, but want me to think they're clever because they dug up some fossil of Sir Isaac Newton dating back to alchemy times....to say nothing of old Pythagoras! Better not like those guys, more than you're supposed to!....seriously, though, even some of the 'popular' science stuff often ends up being, either just--not--popular, and/or some memoir of a fossil hunter to himself, to remind himself how clever and *in touch* he is...it's true that sometimes you do see a science guy that doesn't talk like a moron--maybe the best example for me would be old Mr. Terrazino from high school, a funny old man, and a gifted storyteller, who appreciated a joke--but, in general, I don't think it's the sort of thing that deserves much applause at this point...I mean most of the science books end up being either pseudo-political books about how their universities and university departments aren't sufficiently pampered, generalized whining about how they don't get enough air time on Letterman--even though the only result of attempting to satisfy this demand is to mess up Letterman's show--and the 'popular' books, which end up usually being smarmy semi-memoirs by noisy nobodies who aren't as special as they make themselves sound, and who are far more interested in getting *in the black* by being 'popular', rather than by changing their tone of voice in order to talk to other people...)

Anyway.

And I guess I also learned that math guys can be more more than just crazy old men in golf carts...(tangent: I think golf is trying to rehabilitate its image too, but, personally I'm still rooting for it to crash into the Isle of Skye and die....I mean, I think I still am...Yeah, I think I am. Seriously: the only Scottish person that I like is Andy Murray, so William Wallace can take his empire of sand traps and stfu...along with minature golf and bingo night...because golf courses are ugly, and gold clubs are ugly, and so are golf...golfers...Math is okay though; numbers are nice and primordial.)

Anyway, he does a solid job writing the sort of book he wanted to write.

And, yeah, I get it, Newton, Leibniz--special guys. And hell, I'll forgive, I'll forgive anyone...except for Descartes. I hate that guy. I like it when Witty kills him. ;) (--Eh, but I need him to help me plot the points on this graph I'm making! --Fine, fine, then you can have him too....but don't anybody try to explain to me that Russell may have been useful for something too; I despise Russell. What a lousy friend, and a bad philosopher....like an *evil sibling*!!!)

And, you know, at least he's not like Sheldon. "I'm going to make this as difficult as possible." *laugh track* Because I seriously do think that I'm going to give up on "the rock people", not to mention the give-me-a-billion-dollars-for-an-atom-smasher, or-I-die crowd. ("Hey, but you don't even know how much atom smashers really cost!")

{Tangent: Although, that's actually a good example of what's so wrong with a certain sort of sob story we always hear about 'the media': Sheldon didn't *create* the physics freaks after all, so it's not as though Comedy Central were responsible for the self-inflicted wounds of the science department...}

{Tangent: Although I notice that if someone's *really* clever, and smart like a moron, whenever you tell them something that they need to hear, and can't really deny, they'll just drag some irrelevant rock into the conversation, and then act as though they'd just built Stonehenge, and all to avoid the *consequences* of the truth, a little manipulation which I cannot help but describe as being almost--theological!-- in the brilliance of its ineptitude...}

(N.B. I don't want to juggle words more than I have to, honestly, but the book really is about mathematicians as much as mathematics, so kindly forgive me my transgressions & tangents.)

Anyway....

But maybe these math guys will add up to something....

It is a good book.

And, hey, maybe I should get over myself and give it that extra point, since it really is better than I had any right to expect, even though this sort of thing does give me pain.....

But, hey: "If you take two piles of leaves and add them to a third, the result is not three piles of leaves but one large pile. And if you have just watched a rainstorm, then, as Wittgenstein said, 'The proper answer to the question, 'How many drops did you see?,' is *many*, not that there was a number but you don't know how many.' "

And Wittgenstein is like a storm with many raindrops.

And the thing that I always kinda liked about the math guys was how they could dismiss arbitrarily-large numbers as unimportant, you know?

Oh, a number with 72 digits, well, at a proper level of abstraction, there are *probably* only, like, 2 digits.....

("It doesn't really matter what the trillionth digit of x is...")

That's kinda nice. ^^

And, after all, it is possible for people, (men!), to be put to a proof, and to come through it.

And, you know, the really funny thing is that Nature (Pythagoras or Numa greeting the goddess of the dawn), is, in a way, closer to a certain sort of technical writing, than "science", (knowing!), but, either way, math is certainty ahistorical...although the historians can take heart, since math can at least be *distorted* by history....as I'm sure the great occult master Isaac Newton could tell you....(and he was a contemporary of Locke!)

*But*, I drift from the point at hand, of course. What I really need to say here, is just that it's a very good book, that's written in a clever way.

Okay, one more:

"a statement is obvious if a proof instantly springs to mind."

Now that's fucking funny! *Dios mio*, maybe intellectuals aren't *all* useless gits after all! This is great!

I'm really serious!

(Although the jury is still out on the litcrits, and some of their authors....)

(And math is a little too Greek, sometimes, for my own liking....although I suppose that really is where they surpass my own provincial people! A-hahaha! Who says that Livy is a provincial? He comes from a small town out in the provinces, it is true, and he loves his mother, as all good provincial boys do...but that doesn't make him a provincial! Juno's mercy, no! Well, yes. And a pleb, too, come to think of it. Too bad *I'm* not a pleb... I think that things would have gone ever so much better, that way....Ah, but what use it is, even alluding to that ugly brute! Well, maybe not 'brute', you know....but ah, cruel world, how long will we have to suffer this sort of impudence? Such indecency....politics is such ungentlemanly business, anyway, all those soldiers, so *rough*, just think of what they did to Corinth, just think of what they did to me! No, Juno's mercy, no, they're not *my* kind of people....I prefer the quiet life, the good life, all I want is my little library and my garden, that's all I really need, out here in my little corner of Italy....)

OMG, Oh My God, Oh My God.....Oh My God.

I'm so sorry, you guys. I really am.

Anyway.

And, okay, I'm just going to be a *little* obnoxious here, and add just ONE more thing:

"Mathematicians often talk about what happens 'in the limit,' or 'at infinity,' but they are aware as they do so that they are not being wholly serious. If pressed to say exactly what they mean, they will start to talk about approximations instead."

Stuff like that is what makes this book as good as it is. And:

"The area of the shape is the one number that I cannot disprove."

That's so great, and I'm not even sure exactly what it means. ^^

And, you know, the *best* aspect of the whole thing, really--because I DO notice this sort of thing, and it's THERE, in the WHOLE thing, if you look for it....he even uses cleaning house as an example at one point, and he's so fucking clever about it, you wouldn't even *notice* that that's what he's doing, unless you're fucking obsessed the way that I am--is also what pisses me off about the whole thing....as though I wanted to hear about it, just because I went looking for it, right? Would that make me conflicted, do you think? Yeah, "conflicted" is probably a more relevant word than "ironic", or whatever, for me...

Although I found the comment about fucking Laura Roslin to be a little excessive, even for me. :P

So I'll spare you any attempt to try to make a cute metaphor out of the....hyberbolic disc?--mostly because I myself do not have the stomach to do so....

Although, to be honest--as much as it makes me cringe to do so--I suppose I wasn't actually anything to Mathematica, until all of this happened to me.

And although I do still think that Russell and Platohead were the *devil's* couple--I tell you, they are almost *conspired* against guys like me!--but, since I don't want to sling my accusations around *too* wildly....Gauss was really quite alright. He climbed mountains....and that is where you find the pure air, in the mountains, in the north, *beyond the ice*....far away from *southerly* winds (Plato!). And he was also the guy who was good at counting things, right? I mean, *really* good! (I mean, one of my teachers told me the story about how the guy counted to 100 really really fast--and that was during one of the times when I *almost* became really really interested in math--but obviously Gowers here doesn't repeat the story, since to do so would be to practically ruin the whole point of the entire fucking book....and, believe me, I know *exactly* how he must feel....which is not to say that he's not somewhat (FAR!) more skilled with the whole matter than me, since I (still!) have a tendency to get...*pissy* about things sometimes, even though that's *probably* counter-productive....

But I don't care; I will *never* like soccer--I don't care if every girl in the world plays it! Go play tennis, damn it! *waves fist*

And, I'm not sure if this is *strictly* relevant, but Caroline Wozniacki is *still* Number One In The World, and I don't give a *damn* what *anyone* says about it, *including* Vika....

But, now, if *I* were the Roger Federer of math....*giggles* ("Hello, my name is Roger Federer, and you're watching Math Channel--where numbers live.")

(And my wireless has a radius too....and to be outside it, is to be lost on the edge of eternity....Juno's mercy....Juno's mercy....)

And, you know, Jon Lovitz is like the Timothy Gowers of tennis....

And, you know, Gowers is so *obnoxiously respectful* to *certain people*, it's *almost* as though he's trying to throw me under this bus! Not that I wouldn't do the *exact same* thing, given the *opportunity*, ("It's him or me!"--well, *shit*, that's easy....), but it's a little different when it happens to me.

It's only supposed to happen to *other* guys. ;)

Anyway.

And, basically, I still rather fancy the idea of going off to live in the forest with the wild things and the fey spirits.....

Unless, of course, that would interfere with my nuptial happiness....so it depends, you see.

And ice may be the broad bridge, but I will see myself across it!... After all, constraint gives scant choice. *shrugs*

Although if you guys have to hate me now, I understand that too.

Anyway.

I suppose this might be more useful than pretending to learn Russian, after all. (Although not as useful as pretending to learn astrology....what I mean is, when you try to be as broad as *this*--refers to his crap--you're really only *pretending* to learn things.)

Anyway.

So, anyway, guys, *Jon Lovitz voice*, if finding the *real* answer is too *hard* for you, approximate:

"Above, I have written an exactly correct expression for (it), but does that make you understand (it), better than the information that (it) is about seven and a half?"

And if that's too hard, *guess*!:

"I well remember my first shock when I first heard a mathematician declare that the exact value of a certain quantity would never be known. Now I am used to the fact that this is the rule rather than the exception."

*Novak Djokovic voice* Nine! It's number nine.

*Jon Lovitz voice* No, *loser* it's number ONE!

*Novak Djokovic voice* How am I a loser? I'm the best tennis player since Rod Laver!

*Jon Lovitz voice* But are you NUMBER ONE IN THE WORLD, *Serbo*?

*Caroline Wozniacki dancing*

*sigh* After all, all of the greatest mathematicians have been Danes...even Euclid. (*Novak Djokovic voice* You see, Euclid's father may have come from Poland, but he himself comes from Denmark, and he considers himself a Dane, even though he lives abroad, in Monte Carlo....and those are not anachronisms, they are....feminizations.)

Love is holy madness. ;)

But, consider one more mathematical paradox, as it relates to population growth (refer to page....)--Caroline Wozniacki is Danish, a Nordic, and Novak Djokovic is with the ATP World Tour, masculine--so if you put them together, what would you get?

That's right--a Viking. (Maybe they'll name him Vikingr!)

Hail to the hammer, guys. *clinks glasses*

But seriously....If Tyr, Mars, Odin, and Thor are sharing a barrel of ale (of certain dimensions), how much ale will Tyr get to drink, before the barrel is empty?

Depends! *laughs*

All I know for sure is, that that's stuff's way too intense for me! *laughs* I mean, I thought that once I left Euclid behind in Greece, that *I* would be the one who would know all the math, but now Odin has disproved Euclid, Minerva is trying to take my job, and I still owe that guy that money for that thing....*finishes lacing up his winged sandals*. *Stands up* I tell you, the world is a tough place sometimes, for a little guy like me!

Oh, man, I'm so sorry, you guys, oh my GOD....

*walks off into the land, singing* "Gone is the summer...What will keep us, warm in the winter? Tales of those who died, sword in hand, in times gone by....Hail to the hammer...."

*trips over a stick, and falls flat on his face* "Juno's mercy...."

Anyway, I do apologize for the unusual size and irregular shape of this....rectangle. ;)

But anyway, I hope that we can all agree, even if I'm too southern for the northerners, too northern for the southerners, and not *quite* part of Juno's club, or Thor's drinking companion....

That the forces of nature are out there, and they don't need Thuycicdides....

(Because, after all, if you deny Nature, she denies you....if you deny Nature, then you reject *everything*, and affirm *nothing*, and end up unhappy, and a mess....and, really, despite Tim's apology-ology--and it really does amaze me sometimes, what *bullies* certain people are in Acadeemia (as opposed to 'San Deemas'), about certain things, anyway, just because of what they *claim* to be--or my little temper tantrums--I suppose you can either let yourself fall into suspicion, or just try to accept that it irritates me sometimes, to have it be *assumed* that I am what I am not, far beyond my poor power of patience--it still remains, I think, that it makes little sense to demand that math and philosophy--and as for 'science', ha! 'Science'!--react in the same way as fiction or 'Literature' (historical literature! But what about historical *fiction*, eh?) or novel-writing does, to the people who obsess me....clearly they are different, both in theory and in practice, and I'm not going to feel guilty for whatever small accomplishments I may or may not acquire--and if I find anything, *you* yourself may decide if I win anything by it, if you are who I'm speaking of....waiting for!....but I won't feel *guilty*, either way, unless you can prove to me that my name starts with Bertrand and ends with Fucking Russel! And anyway, as he *almost* admits--he admits the anonymity of it, at any rate--that these *masculine* subjects are anonymous, and nobody minds that, not even the men, that's what really *masculine* men actually *want*, at least sometimes--team sports! theologians!--but they are certainly more anonymous than *almost all* women would *ever* want to be....I mean, Gauss could count, we can all see that, but there was never anything *unique* in anything that he could do, the way there is with the work of Jane Austen or W. B. White....and, in a way, that IS why it's good for the boys, after all! After all, one does not secure "equality"--what a foolish word, sometimes!--in *coal mining*, for example, no!, one passes laws *subtracting* all the women and all the children. Nor does one siphon off players from the WTA to form a WNHL....but, of course, it is *perfectly beneficial* for there to be women who are mathematicians *every so often*, just often enough to help remind the boys that they're really not *so* special, after all....but, whenever you are looking at the *big* picture, the only way to go from, say, 5%, (and in the military, I think, it is closer to five than fifty! And I wouldn't complain!), to upwards of 1/3, or perhaps even *past* 1/2, is to make things *lighter* to let in *air* and *color* and all the things that boys *don't* want, but which women *do*. (The salesgirl told me that boys want black shoes, and girls want color....so I got bright red!) But in anything which has got to be *heavy* and *diffficult to lift* for some reason, even acquiring, say, 5-10% is not nothing, it's an important component, and, in a way, it is *shocking*--Imagine 10% of *military historians*! It would almost be too much!!!....And anyway, in the sociological chapter, he also describes why math class sucks, and rather well, too....and it's almost *more* important, than even what obsesses me....since, after all, if the road to the coal mine's flooded, *nobody* is going there....at all!)

(And yes, I realize that the way I write makes it difficult to read, sometimes. I *do* try to cultivate a good style, but I *do* also realize that sometimes the flaws go deep. My apologies.)

(To be fair, though, it really is EVERYWHERE, in everything from how he brings *even* numbers into his discussion of *prime* numbers--!--to how, when going over the amateurs he ***automatically*** places the housewife first, and the German second....and this after he's already discussed the housewife's problem in an earlier chapter, without any noisy bragging about how he was including a woman's work....although *I* certainly knew enough--was in a position to know--to be, well, "suspicious" ;)....men do not discuss kitchen tiles....not ***before*** we sell out, anyway, says the boy with the bright red shoes....almost pink, really! Honorary pink, perhaps....)

Even if some things are convention, but then, you can be a philosopher and a mathematician, (especially if you're a dude, an airy-fairy sort, one of Juno's birds, or Odin's ravens....or just, the brother of the wind god), but you don't have to be both at the same time.

You can be a little schizo about it, like Witty himself, and there was a great man, and a great smasher of deluded false belief. (Do you want to be a philosopher with a hammer? Then, hail to the hammer!)

But, you know, like Socrates, I know nothing....I don't even know how to fucking shut up, I guess! :P

And, you know, I think that if I were *really* clever, I'd be able to pull off some sort of Real Housewives tie-in (Juno's show!), but....you know.....

(Actually, though, the New Jersey ones are really weird, and I live in New Jersey, but it's like a different planet....those old-school types really didn't believe in love, did they? I like RHOC, though....it's nice to know that not everybody in California is a hippie....they're just *cosmopolitan*....which is almost *opposite*, in a way, lolz....)

Like, how can we even make sense of that number? It's so large, oh my god, what do we, like, even do with it? Oh my god.

I dunno. Let's start by counting the number of digits it has. onetwothreefourfive, Gone is the summer, sixseveneightnineten, What will keep us, warm in the winter, eleventwelvethirteenfourteenfifteen, shit, this number is, like, really big. It has so many digits. I think that it would take a really long time to, like, count all of them.

No shit, genius, oh my god. I'm going to, like, call Kathy and tell her I'm with a *moron*.

(I thought you said he could count quicker than Gauss!)

OO LA-LA, YOU'RE MY SUPERSTAR, OO LA-LA, I LOVE THE WAY THAT YOU ARE.

Why, thank you, girlie. *puts hand on his chest*

Seriously, though, all of the Nook commericals are obviously targeted at women, I, like, want to file a complaint, okay? ^^

Well, okay, I won't if you won't. ;) (Just like in Hamlet!)

Do you think that Caroline will want to get married at Elsinore, or Monte Carlo?

Let's make a graph.

Will she appreciate the importance of alliteration?

Let's invent a algorithm, or something.

^^

Oh yes. I'm crazy. I'M CRAZY.

(9/10) ( )
  Tullius22 | Jun 9, 2012 |
Näyttää 1-5 (yhteensä 7) (seuraava | näytä kaikki)
"Anyone who has wondered what mathematicians do will find this volume illuminating, and those school maths students who occasionally raise their heads from learning formulae long enough to ask "Why?" and "What's it all for?" will find many of their questions answered here."
 
"He has done a wonderful job in producing this rich little book on the essentials of mathematics."
 

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Englanninkielinen Wikipedia (4)

The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?")

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