There's a randomised counterpart to the Sieve of Erathosthenes called the Hawkins ransom sieve: Delete the number 1. Mark two as prime, and delete all the larger integers with probability 1/2. Now mark the smallest remaining integer (n, say) prime, and delete all the remaining larger integers with probability 1/n. Proceed ad infinitum.
One of my favourite results in mathematics is that the Riemann hypothesis (i.e. the error bound for the prime number theorem) holds for the Hawkins random primes with probability 1. The proof is only about five pages:
Z(s) = 1 + 1/(2^s) + 1/(3^s) + 1/(4^s) + ...
is equal to the infinite product over the terms "1/(1-p^(-s))", with one term for each prime number p.
This proof does not need a lot of math , and if you know the formula for a geometric series, you can also "prove it" by hand-waving: Each term in the product is a geometric series, and if you multiply all these series out, the result is a sum over all possible permutations of prime-factored numbers (well, the inverses of them). Since each natural number has exactly one such represnetation, it's effectively a sum over all 1/(n^s).
Of course, you need some rigor to show that you are actually allowed to rearrange terms of an infinite product of inite sums like that...
The problem itself is amazing (even though I don't really understand it). The infinite series is so simple, but it generates so much interesting complexity when you look at it visually:
The Möbius function, defined by http://mathworld.wolfram.com/MoebiusFunction.html, shows up in various sieving operation. It is 0 for a random integer with probability (1 - 6/pi^2) and otherwise has apparently even odds of being +-1.
Its sum is called Mertens function, see http://mathworld.wolfram.com/MertensFunction.html. The Riemann conjecture is equivalent to saying that the growth of Mertens function is o(n^(0.5+e)) for every e > 0. For a long time it was thought to be bounded above by n^0.5, but this is known to be wrong.
If you replace the Möbius function with a function that is -1, 0 and 1 with the right probabilities, then with probability 1 it is O((n * log(log(n))^0.5). Which would prove the Riemann hypothesis. (This intuition would have kept Mertens from conjecturing that it is bounded by +-sqrt(n)...)
I'm sure it would work good even with less or no "trolling." It is possible to make the approachable text even without the jokes based on misinformation. I see the author made the book with that in the title, so it was obviously a selling point for him, but the quite clear approach to the math material (when he reader manages to ignore the trolling) is actually good. I have nothing against the funny presentation of the actual biographical facts however.
The misinformation is, however, problematic. The author even states in the foreword that he "hopes that some of those will appear in Wikipedia." Unfortunately, it really can happen.
If education matters, and if human intelligence augmentation matters, then we should be researching how to make difficult technical material more easily digestible, for example by enhancing it with an appropriate level of humour.
Millions of dollars are being spent on making machines more intelligent (or is it billions?). Someone should be spending some time, money and effort on making people smarter.
Also, compared to other possible human intelligence augmentation technologies, writing textbooks in a more humorous style is less intrusive than taking "smart pills" or placing electrodes inside your brain.
Though humorous style is less intrusive than taking "smart pills" or placing electrodes inside our brains, it is very context-sensitive. I believe humour should definitely be used more often in oral presentations of complicated material, where the presenter is able to "feel" the context of those listening; but maybe not so much in written text.
To make a point, there are many technical textbooks that use funny examples and exercises as a way to draw students attention - and that does generally work quite well - but it can be quite a tiring read if you are going through the material multiple times.
you might like it :)
I absolutely adored Dave Barry's work when I was in middle school (I often couldn't read a single paragraph aloud without laughing out loud) but I find it less enjoyable today. Maybe my taste in humor has shifted somewhat.