It might be Paul Halmos. In his "automathobiography", titled I Want to Be a Mathematician (Springer 1985), page 156: "In the late 1940's I began to act on one of my beliefs: to stay young, you have to change fields every five years". He goes on saying "I didn't first discover it and then act on it, but instead, noting that I did in fact seem to change directions every so often, I made a virtue out of a fact and formulated it as a piece of wisdom".
I wasn't familiar with this painting, for the very good reason that it doesn't exist
Are you sure? The wikipedia page on Flaubert's novel says: "In 1845, at age 24, Flaubert visited the Balbi Palace in Genoa, and was inspired by a painting of the same title, then attributed to Bruegel the Elder (now thought to be by one of his followers)." And the National Gallery seems to think they have it in the West Building (https://www.nga.gov/collection/art-object-page.41602.html).
But somebody has to write those Stackoverflow answers. Perhaps for those who do the distinction between man pages and info is important. Or do you think that the source of Stackoverflow answers is just more Stackoverflow answers? Now that would be hilarious.
It's not pointless, but the outline only shows up if the generated tex file is compiled twice. The default org to latex export will only compile it once.
Alternatively, it is easy to suppress the outline slide altogether (add "toc:nil" to "#+OPTIONS:").
I don't understand the reference to Gödel. Do you mean the theorem that in every formal system capable of representing arithmetic there exist sentences "P" such that neither "P" nor "not P" are derivable in the system?
It doesn't seem to me that from this it follows that "the point of philosophy is better living". It might be obvious, but I just don't see it.
I like to think of it as all formalisms are tautologies. Therefore we can go along with some common sense and fuzzy logic rather than having to prove every possible axiom, which isn't actually possible or would take unlimited time. It's analogous to the halting problem.
You don't always get a prime. For example, 4! = 2 * 3 * 4 = 24, 24 + 1 = 25, 25 is not prime. The point is that N! + 1 is not divisible by any number from 2 to N (always leaves a remainder of 1), so either it is prime, or it is divisible by something larger than N!, therefore larger than N. In the case of 25, it is divisible by 5 (> 4).
Right, but if you were testing N=13 as the highest prime, then (2 * 3 * 5 * 7 * 11 * 13) + 1 must either be prime itself, i.e. have no prime factors, or must have a prime factor greater than 13. And in either case, a prime greater than 13 exists - in your example, 59.
This is Euclid's proof [1] and it's some 2300 years old.
It's a little bit more subtle. Assume that there is a finite number of primes, and P is the set of all primes p0, p1, p2... pn. If you multiply all these together and add 1, you have a number Q that's not divisible by any number in P. So P cannot be the set of all primes.
