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27 points

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27th Oct 2019

William Dunham has a great book,Journey through Genius: The Great Theorems of Mathematics, about this.

2 points

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3rd May 2021

This is a good book about the basic history of math. I had to read it for an undergraduate elective but ended up liking it very much because it gave me a new appreciation for all the amazing discoveries that you're asking about. The book is short and concise and reads like a popular science book rather than a textbook.

Some of the ancient mathematicians had genius brains that just work differently than common brains. And others spent a lot a lot a lot of time carefully drawing and measuring and calculating. Same as doing a long division problem these days on paper instead of using a calculator--more time-consuming but still doable.

2 points

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16th Sep 2020

This is not as much to learn math than to understand the beauty of it: Journey through Genius: The Great Theorems of Mathematics

1 point

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11th Jun 2022

And to add to this, if you want even more history I would also recommend this book. While it can get a little complicated at times with the mathematics, the actual historical context is very clearly written and I think and excellent read if you are interested in how mathematics has developed and some of the most important results.

1 point

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21st Feb 2021

I second this. One book I recommend as introductory is Journey Through Genius. It gets across the axiomatic method, a nice selection of proofs from Elements, can be appreciated by novices and mathematicians, and has a lens of "genius" which may appeal to OP's "sacred" interest.

1 point

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28th Dec 2020

For a (relatively brief) introduction to Cantor and some of his ideas, I'd recommend the relevant chapters of the following:

William Dunham

1991

ISBN-10: 9780140147391

ISBN-13: 978-0140147391

I don't recall the biography there of Cantor to be especially detailed, but this should be an accessible an introduction to some of his mathematical ideas, especially for a lay audience.

Good luck with your project!

1 point

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29th Feb 2016

Journey Through Genius by William Dunham sounds like it would be perfect!

This book layed out such that each chapter takes you through the proof of a famous and important theorem in mathematics and puts it in its historical context and is full of amusing anecdotes while still being packed with actual mathematics.

It should be completely understandable by someone with a basic knowledge of calculus but does require some thinking to follow along with the steps of the proofs. It's also not too intimidating to look at and that makes a big difference for actually working your way through it.

1 point

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25th Feb 2013

I'm currently reading http://www.amazon.com/Journey-through-Genius-Theorems-Mathematics/dp/014014739X/

From ancient Greece all the way through the 15th/16th century theorems such as this were all done with such methods, as the algebra that we know and use today didn't exist. It was all "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides." If you think that's fun, try reading the proof. It gets more interesting when you start getting into cones, etc.

1 point

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27th Mar 2012

I got halfway through your post and immediately thought of Journey through Genius. It really is an excellently-written text which presents precisely what you're looking for. I'd definitely check it out.

1 point

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11th Jun 2012

Appears you need to pick up a "History of Mathematics" book of some sort. I don't have any particular recommendations other than possibly looking into something like this

1 point

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10th Nov 2010

Hi **highly** recommend "Journey Through Genius" by William Dunham. I read it at about the same age. Each chapter covers a mathematical theorem or idea, and provides historical context along with an explanation and proof. It goes from the ancient Greeks to Cantor's dealings with infinities. Clearly written, lots of pictures. I loved it.

1 point

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27th Dec 2020

1 point

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26th Oct 2020

Journey Through Genius is a great book

1 point

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22nd May 2019

I read this book https://www.amazon.com/Journey-through-Genius-Theorems-Mathematics/dp/014014739X and programming helped!

1 point

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30th May 2019

OK: so it appears 4,000 words is (roughly) 8 single-spaced pages at 12 point font. I'm assuming "ib" here means the International Baccalaureate program, too. So: roughly high-school level (or its international equivalent), but with high academic standards. This helps give me a starting point about where to begin.

I still have some followup questions. You may get perfectly good suggestions without providing answers to the following, but I figure it's worth asking nonetheless, if only to clarify your own criteria for what to consider.

- Who is your intended audience?

Are you writing this for a science class? An English class (or other primary language class if English is not your primary language of instruction)? A math class?

- What are the given parameters for this essay, other than what you've already told us?

For example, does this have to be expository? Original research? A synthesis between the two? A historical overview of the development of ideas or academic controversies surrounding them? Are you expected to present an introduction to a topic or rather a detailed exploration?

- When is your assignment due?

The sooner your essay must be turned in—or, for that matter, the sooner you'd have to commit to a topic/thesis/whatever—the less time you'd have to teach yourself new material. That would suggest you ought to select a topic with which you already have some familiarity.

While I'm interrogating you, let me also recommend a book you might find interesting, both in its own right and as a possible source for inspiration for your essay:

William Dunham

Penguin Books

August 1, 1991

ISBN-10: 9780140147391

ISBN-13: 978-0140147391

ASIN: 014014739X

There are a number of genuinely interesting topics here which should be accessible to someone with your background. Topics that stand out for me include Euclid's proof that there are infinitely many primes, the divergence of the harmonic series, and Cantor's diagonal proof that, in a way that can be made rigorous, there are <em>different sizes on infinity</em>. (I don't think this particular book explores it, but there was plenty of academic controversy at the time concerning Cantor's ideas.)

Just for emphasis: none of the topics in *Journey Through Genius* may end up being appropriate for your essay. Still, this seems a useful starting reference, if only to spark your sense of inspiration.

Again, good luck with your final essay and in your IB program more generally!

1 point

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24th Jun 2018

Emphasizing proof, Journey through Genius: The Great Theorems of Mathematics by William Dunham may interest your friend. Dunham provides a very readable historical, conceptual, and formal review of classic theorems. On the philosophical side, Philosophical Devices: Proofs, Probabilities, Possibilities, and Sets by David Papineau may do. It is a first year undergraduate text reviewing set theory, notions of truth, probability, and formal systems. Happy reading to you and your friend!

1 point

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20th May 2017

Journey through Genius: The Great Theorems of Mathematics - Willian Dunham

Very accessable walk through of about a dozen famous proofs from Euclid to Cantor.

1 point

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15th Jun 2016

1 point

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19th Oct 2015

Journey Through Genius might be something worth looking into, although it may not completely satisfy what you're looking for.

http://www.amazon.com/Journey-through-Genius-Theorems-Mathematics/dp/014014739X

1 point

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28th Apr 2015

1 point

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12th May 2011

Journey Through Genius has a pretty good section on Euclid too. http://www.amazon.com/Journey-through-Genius-Theorems-Mathematics/dp/014014739X/ref=sr_1_1?ie=UTF8&qid=1305159225&sr=8-1

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