Reddit reviews Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
We found 19 Reddit comments about Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Here are the top ones, ranked by their Reddit score.
Plume Books
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!
he means this
God Created the Integers, edited by Stephen Hawking. Includes selected works of various big names in mathematics with a brief biography of each preceding the math. The wiki article on the book has a list of all mathematicians included.
Prime Obsession, about Riemann and his famous hypothesis.
The Man Who Knew Infinity, about Ramanujan.
Downmod any math-phobic comments.
Besides, the poster, John Derbyshire, knows his math.
Some good readings from the University of Cambridge Mathematical reading list and p11 from the Studying Mathematics at Oxford Booklet both aimed at undergraduate admissions.
I'd add:
Prime obsession by Derbyshire. (Excellent)
The unfinished game by Devlin.
Letters to a young mathematician by Stewart.
The code book by Singh
Imagining numbers by Mazur (so, so)
and a little off topic:
The annotated turing by Petzold (not so light reading, but excellent)
Complexity by Waldrop
Not a scholarly article, but I like this book https://www.amazon.com/Prime-Obsession-Bernhard-Greatest-Mathematics/dp/0452285259 and think it does a decent job going into the history and attempting to explain the math in a way that doesn't require a grad degree.
These might interest you:
Poincare's Prize
Prime Obsession
Fermat's Enigma
The Code Book
Yes, they do! On average at least. Intuitively, as you get bigger and bigger there are more and more primes with which to make numbers, so the need for them gets less and less. This is answered by the Prime Number Theorem which says that (on average) the number of primes less than the number x is approximately x/log(x). Proving this was a triumph of 19th century mathematics.
Now, this graph of x/log(x) is very smooth and nice, so it only approximates where primes will be. It's not a guarantee. Imagine the primes as a crowd of people in an airport terminal. The crowd is, in general, flowing nicely from the ticket agents to the gate and this appears to be very nice when we look at it from high above. But when we get closer, we see some people walking from the ticket agents to the coffee shop, against the flow. Some kids are running in circles, which is not in the "nice flow" prediction. These fluctuations were not predicted by our model.
So even if primes obey the law x/log(x) overall, there are still fluctuations against this law. While the overall trend is for primes to get infinitely far apart we predict there are infinitely many primes that are right next to each other, totally against the flow. This is the Twin Prime Conjecture. We have recently proved that there are infinitely many pairs of primes, both of which are separated by only ~600 numbers. This was a huge deal and was done only within the last year or so, but we want to get that number down to 2.
We can also ask: "Do these fluctuations affect the overall flow in a significant way, or are they mostly isolated events that don't mess up the Prime Number Theorem approximation too much?" This is the content of the Riemann Hypothesis. If the Prime Number Theorem says that primes are somewhat ordered nicely, then the Riemann Hypothesis says that the primes are ordered as nicely as they can possibly get. That would mean that even though there are variations to the x/log(x) approximation, these fluctuations do not mess things up that bad.
Now, when looking for large primes, we generally look at expressions like 2^(n)-1 because we have fast algorithms to check if these guys are prime. But, in general, most primes do not look like that, they're just very nice numbers that we can check the primatlity of. We do not even know if there are infinitely many primes of the form 2^(n)-1, called Mersenne Primes so we could have already found them all. But we are pretty convinced there are infinitely many, so we're not too worried.
I don't know what your background is, but I've heard that the Prime Obsession is a good layperson book on this (though I haven't read it). If you have math background in complex analysis and abstract algebra, then you could look Apostol's Introduction to Analytic Number Theory.
First saw this in John Derbyshire's Prime Obsession book. Quite beautiful.
For books that will help you appreciate math, I recommend Journey Through Genius by William Dunham for a general historical approach, and Love and Math by Edward Frenkel and Prime Obsession by John Derbyshire for specific focuses in "modern" mathematics (in these cases, the Langlands program and the Riemann Hypothesis).
There's a lot of mathematical lore that you'll find really interesting the first time you read it, but then it becomes more and more grating each subsequent time you come across it. (The example that springs most readily to mind is how the Pythagorean theorem rocked the Greeks' socks about their belief in numbers and what the brotherhood supposedly did to the guy who proved that irrational numbers exist). For that reason, I recommend reading only one or two books that summarize the historical developments in math up to the present, and then finding books that focus on one mathematician or one theorem that is relatively modern. In addition to the books I mentioned above, there are also some good ones on the Poincare Conjecture and Fermat's Last Theorem, and given that you're a computer science guy, I'm sure you can find a good one about P = NP.
I found Prime Obsession really captivating.
I read somewhere (I think it was Derybshire?) that it really should be called a conjecture, but it's been labeled a hypothesis because of its importance/fame.
Edit: nope, here it is.
Here's another.
Prime Obsession
http://www.amazon.com/Prime-Obsession-Bernhard-Greatest-Mathematics/dp/0452285259/ref=sr_1_1?ie=UTF8&s=books&qid=1261458431&sr=1-1
It explains the Riemann Hypothesis mathematically and historically, alternating every chapter. It explains it at a level that people with a decent ability to understand math can follow.
I've not finished it, but I have gotten 2/3rd through and I've really enjoyed it.
Great video! Keep going!
Also, for those who love math, but are not mathematicians (like myself) I could recommend to read the book Prime Obsession by John Derbyshire. It is gonna blow your mind!
https://www.amazon.com/Prime-Obsession-Bernhard-Greatest-Mathematics/dp/0452285259
thanks for the link, anyone who liked this might like (more suggestions welcome)
http://www.bbc.co.uk/programmes/b00srz5b/episodes/downloads
https://www.amazon.co.uk/Godel-Escher-Bach-Eternal-anniversary/dp/0140289208
https://www.amazon.co.uk/d/Books/Prime-Obsession-Bernhard-Greatest-Mathematics/0452285259
As an introduction to Algebra I can recommend https://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773/ref=sr_1_1?ie=UTF8&qid=1486044711&sr=8-1&keywords=Shen+Algebra You may be also interested in https://www.amazon.com/Prime-Obsession-Bernhard-Greatest-Mathematics/dp/0452285259/ref=sr_1_1?rps=1&ie=UTF8&qid=1486042204&sr=8-1&keywords=prime+obsession+derbyshire
Moreover, it would be nice to watch these 'Youtube' channels: https://www.youtube.com/user/Vihart https://www.youtube.com/user/njwildberger
Para quem tiver tempo, recomendo também: https://www.amazon.com/Prime-Obsession-Bernhard-Greatest-Mathematics/dp/0452285259
two excellent books by John Derbyshire:
Prime Obsession regarding the Riemann Hypothesis
Unknown Quantity which is about the history of Algebra