The gist of it seems to be as follows. The Riemann zeta function, defined on some complex numbers, is the function f(x) = 1/1^x + 1/2^x + 1/3^x + ..., which is the limit, if it exists, of the sequence 1/1^x, 1/1^x + 1/2^x, 1/1^x + 1/2^x + 1/3^x, ... . The function is defined on all complex numbers whose real part is greater than 1. If it were defined on -1, then f(-1) would be 1 + 2 + 3 + ..., but it isn't defined on -1, because the sequence 1, 3, 6, ... has no limit. However, there does exist a unique analytic function g such that, for all complex numbers x, if f(x) is defined then so is g(x), and f(x) = g(x), and g is defined on -1. For reasons I don't understand, g(-1) = -1/12, and that somehow entitles one to say that 1 + 2 + 3 + ... = -1/12.

Come to think of it, I don't understand why the Riemann zeta function can't just be considered as a function on the reals, or even the rationals, and then proceed from there. Is it because in that context it does not extend to an analytic function that is defined on -1? Is that why it is necessary to invoke the complex numbers?

The "proof" I've seen is predicated not on the zeta function (which I don't really understand) but on other "proofs" that involve shady manoeuvres like

S1 = 1 - 1 + 1 - 1 + ... = 1/2 (because it yields partial sums 1 and 0 of which 1/2 is the mean lol)

Eliminate the impossible...

It's the not knowing whether a solution even exists. A problem is easier to solve if you know in advance that a solution exists. I keep hoping it's there, a hidden Faberge egg staring at me like the Cheshire cat, but the evidence to the contrary is accumulating. Failure is damaging to one's faith.

Accentuate the positive!

Wow. A kindred spirit. I stop off in the local for a pint, and meet a woman who knows more than me about the A6 murder case, thinks Hangover Square is one of the greatest books ever written, and that Fall Out is the greatest work of art ever. She's called Denis, like in the Blondie song.

It's funny to look back and remember Blondie as being (rightly) adored by the year zero set when quite a few of their hits, like Denis, were covers (very much frowned upon at the time).

What a great band though.

Blondie was part of the canon.

I had to finish early today. Quickest way from Mayfair to Victoria was via Waterloo Bridge. Unless you want to go via Kensington LOL. Some demonstration. I check every Friday whether there is one planned in support of Palestine, which there has been every other Saturday for the past six months, so I'm not sure what this one was. Mexicans in the back. At first they don't get it, but when they see the mayhem everywhere it's "you treated us like a friend", which was a nice thing to say. The aforementioned pub near me is some rare spacetime conjunction of people I like. By coincidence, some hippy gets in at Victoria yesterday, "just a short journey, man", and it turns out he's a friend and neighbour of one the regs. Of course I don't charge him. Gay Pride next Saturday. Legalize it and they start acting like they own the place. Just kidding. Nothing is happening.