Robert Low
@robjlow.bsky.social
Ex maths lecturer. Now classics postgrad (MA) @ClassicsWarwick. Also @[email protected], mostly maths there. Mostly lurking for the moment, haven't yet given up on Twitter completely.
There's this stuff called differential Galois theory, about which I know the name, and that seems to hold the answer. But I don't understand it at all. (To be fair to me, I haven't really tried...)
en.wikipedia.org/wiki/Differe...
en.wikipedia.org/wiki/Differe...
Differential Galois theory - Wikipedia
en.wikipedia.org
November 13, 2025 at 4:34 PM
There's this stuff called differential Galois theory, about which I know the name, and that seems to hold the answer. But I don't understand it at all. (To be fair to me, I haven't really tried...)
en.wikipedia.org/wiki/Differe...
en.wikipedia.org/wiki/Differe...
Well, it doesn't help me :-/
Maybe there's something about the rate at which the coefficients decrease hiding in there, but I have no feel for how that might distinguish algebraic from transcendental functions. I've probably already said strictly more than I know...
Maybe there's something about the rate at which the coefficients decrease hiding in there, but I have no feel for how that might distinguish algebraic from transcendental functions. I've probably already said strictly more than I know...
November 13, 2025 at 4:25 PM
Well, it doesn't help me :-/
Maybe there's something about the rate at which the coefficients decrease hiding in there, but I have no feel for how that might distinguish algebraic from transcendental functions. I've probably already said strictly more than I know...
Maybe there's something about the rate at which the coefficients decrease hiding in there, but I have no feel for how that might distinguish algebraic from transcendental functions. I've probably already said strictly more than I know...
The gate isn't well-defined the cal for boarding. (Sometimes not even then...)
November 13, 2025 at 4:09 PM
The gate isn't well-defined the cal for boarding. (Sometimes not even then...)
Or even "very not-easy-to-define": we still have the problem when everything in sight is analytic. (Hence my 'not really having a clue'.)
November 13, 2025 at 4:08 PM
Or even "very not-easy-to-define": we still have the problem when everything in sight is analytic. (Hence my 'not really having a clue'.)
My first year lecturer said 'Differentiation is an algorithm. Integration is a zoo.'
November 13, 2025 at 3:58 PM
My first year lecturer said 'Differentiation is an algorithm. Integration is a zoo.'
Not really. It's a mystery to me why the derivative of an algebraic function will always be an algebraic function, but the integral may be transcendental (eg integral of 1/sqrt{1-x^2}).
November 13, 2025 at 3:51 PM
Not really. It's a mystery to me why the derivative of an algebraic function will always be an algebraic function, but the integral may be transcendental (eg integral of 1/sqrt{1-x^2}).
Yes - they're only given because they're doable. (One day I'd like to understand properly why differentiation keeps you inside a 'nice' family of functions, but integration doesn't.)
November 13, 2025 at 3:25 PM
Yes - they're only given because they're doable. (One day I'd like to understand properly why differentiation keeps you inside a 'nice' family of functions, but integration doesn't.)
Ooh, that's very different. I considered what f(1) and f(-1) compute for a polynomial, and then combined those values appropriately to get the answer.
November 13, 2025 at 3:23 PM
Ooh, that's very different. I considered what f(1) and f(-1) compute for a polynomial, and then combined those values appropriately to get the answer.
Ah, just get chatGPT to translate it for you. (I wouldn't be surprised if it gave you something it called a translation. In fact, I kind of hope does.)
November 13, 2025 at 3:03 PM
Ah, just get chatGPT to translate it for you. (I wouldn't be surprised if it gave you something it called a translation. In fact, I kind of hope does.)
Selkies are what gave rise to the mistaken notion of mermaids.
November 13, 2025 at 3:00 PM
Selkies are what gave rise to the mistaken notion of mermaids.
To be fair, it was probably used in the fine classical tradition of ripping a quotation entirely out of context and using it as part of an argument it had no relevance to.
November 13, 2025 at 2:58 PM
To be fair, it was probably used in the fine classical tradition of ripping a quotation entirely out of context and using it as part of an argument it had no relevance to.
Hey, it was good enough for Jules Verne!
November 13, 2025 at 2:56 PM
Hey, it was good enough for Jules Verne!
I used to tell my students that the standard procedure for integration was to ask oneself 'what does this look like the derivative of?' and work from there. (It's not exactly an algorithm, I know, which did disappoint some of them.)
November 13, 2025 at 2:55 PM
I used to tell my students that the standard procedure for integration was to ask oneself 'what does this look like the derivative of?' and work from there. (It's not exactly an algorithm, I know, which did disappoint some of them.)
Another example of a tedious calculation that can be entirely dispensed with by means of the right insight. Nice.
November 13, 2025 at 1:25 PM
Another example of a tedious calculation that can be entirely dispensed with by means of the right insight. Nice.
I could understand doing that for extra practice (on the assumption that what chatGPT spat out would in fact be 'questions that were like the tutorial questions') but not as instead of. (If it can reliably produce questions 'like' others, it might be very useful for exam revision. Big 'if', though.)
November 13, 2025 at 1:20 PM
I could understand doing that for extra practice (on the assumption that what chatGPT spat out would in fact be 'questions that were like the tutorial questions') but not as instead of. (If it can reliably produce questions 'like' others, it might be very useful for exam revision. Big 'if', though.)
Roly-poly pudding. (Though to be fair I haven't had it in a long, long time, so my memory may be misleading me as to how delicious it is.)
November 12, 2025 at 10:06 PM
Roly-poly pudding. (Though to be fair I haven't had it in a long, long time, so my memory may be misleading me as to how delicious it is.)
Not just every archivist: ever human being with enough sense to come in out of the rain.
November 12, 2025 at 3:10 PM
Not just every archivist: ever human being with enough sense to come in out of the rain.
The only reason Europe isn't covered in collapsed mediaeval cathedrals is that they reused the stone for the next attempt at getting one to stay up. 😈
November 12, 2025 at 2:07 PM
The only reason Europe isn't covered in collapsed mediaeval cathedrals is that they reused the stone for the next attempt at getting one to stay up. 😈
Pretty sure a substantial proportion of Americans (and Brits, for that matter) live in a dream version of their native country, where they've lived all their lives.
November 11, 2025 at 7:40 PM
Pretty sure a substantial proportion of Americans (and Brits, for that matter) live in a dream version of their native country, where they've lived all their lives.
Definitely on a mission from God.
November 11, 2025 at 7:38 PM
Definitely on a mission from God.
For equal amounts of 'oh, wow!', 'easy but wrong' trumps 'requiring thought but right'.
November 11, 2025 at 12:40 PM
For equal amounts of 'oh, wow!', 'easy but wrong' trumps 'requiring thought but right'.
He was probably the one the others were paying to take the notes.
November 11, 2025 at 12:08 PM
He was probably the one the others were paying to take the notes.
Played so fast he didn't notice it was the Odyssey, not the Iliad.
November 11, 2025 at 12:07 PM
Played so fast he didn't notice it was the Odyssey, not the Iliad.
I'm going to make the more charitable assumption, namely that this is a bit of light trolling.
November 10, 2025 at 3:48 PM
I'm going to make the more charitable assumption, namely that this is a bit of light trolling.