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I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament," and found that I, too, lament the uninspiring quality of my elementary math education.

I want to make a book that discredits the notion that math is merely a series of calculations, and inspires a sense of awe and genuine curiosity in young readers.

However, I myself am mathematically unsophisticated.

What was the first bit of mathematics that made you realize that math is beautiful?

For the purposes of this children's book, accessible answers would be appreciated.

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For me Euclid's proof of the infinitude of primes was the first thing that made me realize the beauty of mathematics. –  Manjil P. Saikia Mar 7 '13 at 7:02
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Wow. Just last night I had a fierce argument with one of the bartenders of my usual watering hole who is a mechanical engineering student. He insisted that he has a better idea than me of what is mathematics. I am so going to print him a copy of Lockhart's text. Thank you for that link! –  Asaf Karagila Mar 7 '13 at 7:59
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I can’t remember a time when I didn’t think that mathematics was beautiful and fascinating. –  Brian M. Scott Mar 7 '13 at 15:06
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Although I don't know if it's what you are looking for, try looking up "vihart" on youtube--Even if it's not helpful, I guarantee you will appreciate it. –  Bill K Mar 8 '13 at 2:57
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I think it's a shame that this question was voted closed... –  Will Mar 10 '13 at 19:50

153 Answers 153

There is a series of math children books in Russian by
Владимир Артурович Лёвшин. To list some:
Магистр рассеянных наук (translates roughly as Master (as in M.Sci) of the absent-minded
sciences, though google translates it as Master scattered Sciences),
Новые рассказы Рассеянного Магистра (New stories of the absent-minded Master),
Путешествие по Карликании и Аль-Джебре (google transtales it as Travel Karlikanii and Al Gebre),
Черная маска из Аль-Джебры (The Black Mask from al-ğabr(=al-gebra)).
More of them at http://www.koob.ru/levshin/ (in Russian).

I am a Bulgarian (presently working in New York), and as a child (could have been anything between 6 yr old and 9 yr old) read the Bulgarian translation of Путешествие по Карликании и Аль-Джебре (or it might have been one of the other books listed above).

I was fascinated. At hindsight mathematically the book is fairly simple or even routine (goes on to set and solve an equation, must have been a quadratic one, though it might have even been linear), so once you know how to solve such equations it might appear boring. But amazingly it does it in a way that unfailingly keeps the readers attention. It is written like a detective story (the $X$ with the black mask was enchanted and was to be freed by the Master, and its assistant the Нуличка, i.e. the Naught or the Null), with characters to relate to, number system and operations introduced and, thus, developing in parallel, the necessary math background and an intriguing story to follow and enjoy. I motivated myself to understand the math details (it might have been that we had not yet covered that material in school), so I could keep reading. I was also interested in logic-puzzle books at about the same time. I cannot single out a particular math piece that is exciting in this book (generally it is about real numbers or perhaps integers, setting and solving equations), it is the whole process of taking an ignorant (but intrigued) child and making him willing to follow the story, and to eventually learn algebra (at the level of quadratic equations) on their own, and make them feel great about it (and at the same time to not know at all what exactly feat they have done, that is, there was no feeling at all that I was being educated in "accurate reckoning for inquiring into things, and the knowledge of all things, mysteries...all secrets", to borrow from Ahmes, even if there is no direct relation).

I do not know if an English translation is available of this series (google doesn't seem to know about it, and google knows everything, unless I do not know how to find it). I think this is a great book and would recommend it to anyone who could read it (or, well, would certainly recommend it to children, since adults would be spoiled with what they already know, and might not enjoy it). In my opinion this book has the spirit of adventure, and it might make an interesting reading (it reminds me of another Russian (or Soviet) well-known "adventure" book, The Twelve Chairs, with sequel The Little Golden Calf, though both format and subject are very different, but perhaps one could feel that both represent Russian culture ... don't know what the author(s) would have thought of this alleged affinity though).

I also remember that as a child I had a problem understanding infinity (безкрайност in Bulgarian, literally endlessness), and kept thinking about it. It is not clear if I understood it (it looked like a winding road that kept going no matter what), but at some point I stopped thinking about it. Nowadays I presumably know that there are different related notions: limitless/ boundless / infinite, and different parts of math might have use of one or the other (e.g. manifold without a boundary like the circle, vs the real line which extends both ways, or transfinite numbers which go just one way but could be used for counting). I could not quite accept that infinity exists (and strictly speaking nobody could prove that it does, but anyway it is an accepted convention), my point is that I forced myself to imagine that winding road never-ending, to try to get an idea of infinity, but I don't think I ever convinced myself. I could not see the whole thing, even if any time I approached the end, it kept extending (as I would just generate one more piece of it in my mind and put it there for the sake of the argument), so for me infinity was something that I cannot exhaust by way of observation, but cannot comprehend either. I could not rule out its existence, so I live with that, but I never saw it, so I can't vouch for it. (Much later at university I had a dream, almost a nightmare when I was supposed to pick a rifle from what seemed an endless field of identical rifles, and I couldn't make a choice. Eventually I picked one, its virtue was that is was exactly the same as all the others, but fulfilled the task of picking one. Somehow I tend to relate this to the Axiom of Choice, though strictly speaking you do not need AC to pick just one element of just one set. And I have no idea why it was rifles, and not, say, apples. Also, that was a multiset, not a set, so I don't know what it had to do with AC, I guess I had to come up with something familiar when I woke up, and we had already studied AC. Or perhaps someone could indeed relate this to AC in a meaningful interpretation.)

And of course, I do appreciate things like Euclid's proof that there are infinitely many primes, or that (Pythagoras or Hippasus) $\sqrt{2}$ is irrational (these were some of the first things I enjoyed introducing to my students last semester in a History of Math class), but for me these came "later" when I was already a converted mathematician (or I thought of myself so). I can't tell when this conversion happened, but it might have been in early school. I was good at math (so my teachers were happy and my schoolmates sought my help, and for that matter everyone would keep telling me that my grandmother, whom I newer saw, was a famous (or infamous, because she would uncompromisingly fail bad pupils) math teacher in my home-town), but it is not just about being good at it (as I realized, there were better students than me, once I got into university, in particular some of those coming out from so-called matematicheska gimnazia - a high-school emphasizing math, science and languages), so it is not so much about being good at it, as about being attracted by math, willingness to keep working/discovering, and the adventure and meaning that comes with it.

Please let us know when your book is published :)

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This is rather recent (Less than a year ago), but, since I am 14, I suppose it should still apply. I remember that I was bored in some class, and that I took out my calculator and started playing with it, writing "hello" with numbers upside down. Then I saw this button (this was a scientific calculator) that said "log," and so I pressed it. At first I received "error" for log(0) = -infinity (well, close enough), but then I tried other numbers, 1,2 10. Then I saw that at 10 it would blurt out 1, and at 100 2. I then realized that what log did was find the exponent of a number from a base number (of course, I didn't know that terminology then) but it was still pretty amazing. (I also learned later on that all calculators are log base 10)

Edit: is there something wrong with this answer? Why was it down voted?

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I don't find it beautiful, but I still find the idea expressed by the following something of a psychological curiosity:

How can it be that when some algebraists say "AND" and "OR" they mean exactly the same thing?

OR means this that "false or false" is false, "false or true", "true or false" as well as "true or true" are true, or more compactly:

    F  T
 F  F  T
 T  T  T

AND means this:

    F  T
 F  F  F
 T  F  T

But, since NOT(x OR y)=(NOT x AND NOT y) and NOT(T)=F and NOT(F)=T, OR and AND, to an algebraist, mean exactly the same thing!

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3  
Your answer implies that $\neg ( \perp \lor \top) \iff ( \neg \perp \land \neg \top) \iff ( \top \land \perp ) \iff ( \perp \lor \top)$. Your truth table for $\land$ is wrong. –  Andrew Salmon Mar 23 '13 at 21:10
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@AndrewSalmon Thanks, I don't know how I did that. –  Doug Spoonwood Mar 24 '13 at 2:45

protected by Zev Chonoles Mar 7 '13 at 22:43

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