Reddit mentions of Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem

Simon Singh explains.

edit: Hey, I didn't expect this to become the top comment. Neat. Might as well abuse it, by providing bonus material:

This is the same Simon Singh discussed in this recent and popular Reddit post; he is a superhero of science popularization. He has written some excellent and highly rated books:

• Big Bang: The Origin of the Universe
  
• The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
  
• Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
  
• Trick or Treatment: The Undeniable Facts about Alternative Medicine
  
  (full disclosure: I have nothing to disclose, other than that I'm a fan of his work.)

I enjoyed this one by the same author: Fermat's Enigma. Maybe 1/3 to 1/2 of the book tells the story of Andrew Wiles trying to prove Fermat's Last Theorem (and the significance of it), and mixed in throughout is information about all sorts of mathematical history.

This is not a highly advanced or hard-to-read book. Anybody with an interest in mathematics could enjoy it. If you're looking for some higher-level mathematical knowledge, this is not the book to read. I haven't read The Code Book, so I don't know how similar it is.

EDIT: The first review starts with "After enjoying Singh's "The Code Book"..." The reviewer gave it 5 stars.

Seems a waste not to link to this fantastic book about how he solved it.

I doubt this can be answered for a five year old, I read an excellent book on the subject and still don't really get it. I will try to recount the jist of what I remember.

Fermat left a small note scribbled in the margins of a book: a^n + b^n = c^n has no solution for positive integers greater then 2.

What fascinated everyone is that if n=2 you have the Pythagorean theorem which every knows, loves, and uses all the time. But to say that there is no solution for a^3 + b^3 = c^3 well that seems a bit crazy. You can sit down and try to plug in the first few values yourself, and low and behold you cant find any solution. Fermat had claimed that he had a proof that showed that this was true from 3 > infinity. (personally I don't think he had an actual proof, more of a very strong gut instinct and if anyone in his lifetime proved him wrong he would have laughed at them and said that he trolled them hard.)

That's the background, now to your questions, what are mathematical proofs? They show that a given formula is true in all cases, any two positive integers plugged into the Pythagorean theorem will result in a real solution for C.

Why is it hard to make them? because you have to show that the theorem works to infinity, you can plug in billions of numbers into a theorem, and prove nothing because the billionth + 1 may not be true

What was so special about Fermat's? Not much, except that it drove people insane with its simplicity, but it took hundreds of years to prove that a^3 + b^3 = c^3 had no real solutions and hundreds of years more for Andrew Wiles and Richard Taylor to discover the general proof.

From wikipedia as to whether Fermat actually had a general formula:

>Taylor and Wiles's proof relies on mathematical techniques developed in the twentieth century, which would be alien to mathematicians who had worked on Fermat's Last Theorem even a century earlier. Fermat's alleged "marvellous proof", by comparison, would have had to be elementary, given mathematical knowledge of the time, and so could not have been the same as Wiles' proof. Most mathematicians and science historians doubt that Fermat had a valid proof of his theorem for all exponents n.

and finally my attempt at EILI5:

You know how you ask me a million questions every day, and some times I don't have the answer. Now imagine going to your teacher and asking them, and they don't know, and ten years from now you ask another teacher and they still don't know, you grow up and go to college and ask your professors and they don't know either. Your question sounds like it should be easy to answer, why doesn't anyone know the answer, then you try to answer it for yourself, and you can't figure it out. You try for thirty years to answer the question, and talk to other people who have tried to answer the question for the last 400 years and still no answer. Some people might give up, but the fact that you could be the first person in the world to know something makes you work even harder to find the answer to this simple question.

Computer scientist here... I'm not a "real" mathematician but I do have a good bit of education and practical experience with some specific fields of like probability, information theory, statistics, logic, combinatorics, and set theory. The vast majority of mathematics, though, I'm only interested in as a hobby. I've never gone much beyond calculus in the standard track of math education, so I to enjoy reading "layman's terms" material about math. Here's some stuff I've enjoyed.

Fermat's Enigma This book covers the history of a famous problem that looks very simple, yet it took several hundred years to resolve. In so doing it gives layman's terms overviews of many mathematical concepts in a manner very similar to jfredett here. It's very readable, and for me at least, it also made the study of mathematics feel even more like an exciting search for beautiful, profound truth.

Logicomix: An Epic Search for Truth I've been told this book contains some inaccuracies, but I'm including it because I think it's such a cool idea. It's a graphic novelization (seriously, a graphic novel about a logician) of the life of Bertrand Russell, who was deeply involved in some of the last great ideas before Godel's Incompleteness Theorem came along and changed everything. This isn't as much about the math as it is about the people, but I still found it enjoyable when I read it a few years ago, and it helped spark my own interest in mathematics.

Lots of people also love Godel Escher Bach. I haven't read it yet so I can't really comment on it, but it seems to be a common element of everybody's favorite books about math.

Hey! This comment ended up being a lot longer than I anticipated, oops.

My all-time favs of these kinds of books definitely has to be Prime Obsession and Unknown Quantity by John Derbyshire - Prime Obsession covers the history behind one of the most famous unsolved problems in all of math - the Riemann hypothesis, and does it while actually diving into some of the actual theory behind it. Unknown Quantity is quite similar to Prime Obsession, except it's a more general overview of the history of algebra. They're also filled with lots of interesting footnotes. (Ignore his other, more questionable political books.)

In a similar vein, Fermat's Enigma by Simon Singh also does this really well with Fermat's last theorem, an infamously hard problem that remained unsolved until 1995. The rest of his books are also excellent.

All of Ian Stewart's books are great too - my favs from him are Cabinet, Hoard, and Casebook which are each filled with lots of fun mathematical vignettes, stories, and problems, which you can pick or choose at your leisure.

When it comes to fiction, Edwin Abbott's Flatland is a classic parody of Victorian England and a visualization of what a 4th dimension would look like. (This one's in the public domain, too.) Strictly speaking, this doesn't have any equations in it, but you should definitely still read it for a good mental workout!

Lastly, the Math Girls series is a Japanese YA series all about interesting topics like Taylor series, recursive relations, Fermat's last theorem, and Godel's incompleteness theorems. (Yes, really!) Although the 3rd book actually has a pretty decent plot, they're not really that story or character driven. As an interesting and unique mathematical resource though, they're unmatched!

I'm sure there are lots of other great books I've missed, but as a high school student myself, I can say that these were the books that really introduced me to how crazy and interesting upper-level math could be, without getting too over my head. They're all highly recommended.

Good luck in your mathematical adventures, and have fun!

Fermat's Last Theorem by Simon Singh.

(I'm reasonably sure the linked book is Fermat's Last Theorm, just with a different title. It was the closest I could find on US Amazon)

I picked up the book by Simon Singh at a garage sale 10 or so years ago. Fascinating read. Looking forward to watching the doc now.

EDIT: evidently the book is now called Fermat's Enigma in the US...

Thanks for the suggestions! Just so you are aware the Fermat's Enigma link is a duplicate of Journey through Genius.

Journey through Genius sounds really interesting. I'm curious if you've ever read Gödel, Escher, Bach? If so how would you compare the two?

These might interest you:

Poincare's Prize


Prime Obsession


Fermat's Enigma

The Code Book

Fermat's Enigma by Simon Singh is an approachable history of Fermat's last theorem, various brilliant but failed proofs, and Wiles' ultimate conquest. While it's not technical, the book profiles the mathematicians tormented by Fermat's theorem and details the approaches they used. You may find it helpful as a map or a timeline. Certainly worth reading.

http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622

Maybe a bit off topic, but I think that if you have a "math phobia" as you say, then maybe you need to find a way to become interested in the math for math's sake. I don't think you'll be motivated to study unless you can find it exciting.

For me, The Universal History of Numbers was a great book to get me interested in math. It's a vast history book that recounts the development of numbers and number systems all over the world. Maybe by studying numbers in their cultural context you'll find more motivation to study, say, the real number system (leading to analysis and so on). That's just an example and there are other popular math books you could try for motivation (Fermat's Enigma is good).

Edit: Also, there are numerous basic math books that are aimed at educated adults. Understanding Mathematics is one which I have read at one point and wasn't bad as far as I can remember. I am sure there are more modern, and actually for sale on Amazon, books on this topic though.

When I was his age, I read a lot of books on the history of mathematics and biographies of great mathematicians. I remember reading Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem.

Any book by Martin Gardner would be great. No man has done as much to popularize mathematics as Martin Gardner.

The games 24 and Set are pretty mathematical but not cheesy. He might also like a book on game theory.

It's great that you're encouraging his love of math from an early age. Thanks to people like you, I now have my math degree.

Fermat's Last Theorem is a pretty good story. It's an easy to understand problem that was unsolved for 300 years until ~20 years ago.

There's a book about it and a PBS documentary you can watch for free.

Meh, was a bit anti-climactic.

I preferred Fermat's Last Theorem. That took 350 years to solve, not just a quick google. Kids today etc...

This whole thing reminds me of a book I read a few years back about a guy who proved Fermat's Last Theorem. Fascinating stuff. Really gives one an insight into how beautiful the human mind is.

Even better: [Fermat's Enigma]{(http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622)

And I would recommend any book by Simon Singh any day.

A great book on Andrew Wiles and Fermat's Last Theorem is Simon Singh's Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem.

Another vote for The Code Book, as a book targeted more towards the general public, I thought it was excellent. I read it in high school and it's one of the reasons I decided to go into math/CS in university!

Fermat's Enigma (also by Singh) is another one I enjoyed.

You can start with "Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem" >> http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622 . Is a great book, I read it several times.

Initially I'd avoid books on areas of science that might challenge her (religious) beliefs. You friend is open to considering a new view point. Which is awesome but can be very difficult. So don't push it. Start slowly with less controversial topics. To be clear, I'm saying avoid books that touch on evolution! Other controversial topics might include vaccinations, dinosaurs, the big bang, climate change, etc. Picking a neutral topic will help her acclimate to science. Pick a book related to something that she is interested in.

I'd also start with a book that the tells a story centred around a science, instead of simply trying to explain that science. In telling the story their authors usually explain the science. (Biographies about interesting scientist are a good choice too). The idea is that if she enjoys reading the book, then chances are she will be more likely to accept the science behind it.

Here are some recommendations:
The Wave by Susan Casey: http://www.amazon.com/The-Wave-Pursuit-Rogues-Freaks/dp/0767928857

Fermat's Enigma by Simon Singh: http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622

The Man who Loved Only Numbers by Paul Hoffman: http://www.amazon.com/Man-Who-Loved-Only-Numbers/dp/0786884061/ref=sr_1_1?s=books&ie=UTF8&qid=1405720480&sr=1-1&keywords=paul+erdos

I also recommend going to a book store with her, and peruse the science section. Pick out a book together. Get a copy for yourself and make it a small book club. Give her someone to discusses the book with.

After a few books, if she's still interested then you can try pushing her boundaries with something more controversial or something more technical.

Well, regarding Fermat's Last Theorem, it indeed was written by Aczel, as could easily be determined by following the link in the article. However, it looks like there are 100s of books with a similar name. The one your read by Simon Singh was called: Fermat's Enigma.

You weren't misled, you just "misremembered".

To answer your second question, KhanAcademy is always good for algebra/trig/basic calc stuff. Another good resource is Paul's online Math Notes, especially if you prefer reading to watching videos.

To answer your second question, here are some classic texts you could try (keep in mind that parts of them may not make all that much sense without knowing any calculus or abstract algebra):

Men of Mathematics by E.T. Bell

The History of Calculus by Carl Boyer

Some other well-received math history books:

An Intro to the History of Math by Howard Eves, Journey Through Genius by William Dunham, Morris Kline's monumental 3-part series (1, 2, 3) (best left until later), and another brilliant book by Dunham.

And the MacTutor History of Math site is a great resource.

Finally, some really great historical thrillers that deal with some really exciting stuff in number theory:

Fermat's Enigma by Simon Sigh

The Music of the Primes by Marcus DuSautoy

Also (I know this is a lot), this is a widely-renowned and cheap book for learning about modern/university-level math: Concepts of Modern Math by Ian Stewart.

For those that just think it's funny because it might be something you see in a textbook, it's not just that. This joke is a direct reference to Fermat's Last Theorem, which was proposed in 1637 and the text above was scribbled in the sidebar of the paper. It wasn't actually proven until 1994, 350+ years later.

Interestingly enough, it's unlikely that the current proof, which I think was around 300 pages, was anything like Fermat's proof that he alluded to (and possibly never had, which makes him an amazing troll). The current proof used methods that were not developed until recently, and I believe the author of the proof even developed some new mathematics in order to solve it.

https://en.wikipedia.org/wiki/Fermat's_Last_Theorem

Here's a great book on it, and the guy that finally provided the proof. Definitely worth reading, it's not boring at all: http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622