Thomas Bloom

Royal Society University Research Fellow at the University of Manchester. Mathematician and owner of He/him/his.

[Thomas Bloom @thomasfbloom]

@AlejandroZarUrd If we were discussing this with other alien species, then yes such a modifier should be added. Or if having speculative discussions about what kind of mathematics other species could do.

But these are conversations amongst humans, with humans in mind.

[Thomas Bloom @thomasfbloom]

Mathematics -is- a human endeavour.

There is something which maybe you're calling mathematics that has nothing to do with humans, some 'platonic otherworld' of abstract ideas. But what I call mathematics is the human attempt to explore and understand this world.

[Przemek Chojecki | PC @prz_chojecki]

There are two main points in the Leiden declaration, one good, one bad imho:

> Good: science is underfunded, mathematics included. We need more researchers, not less, and with the advent of AGI we will need even more. If AGI is a magical wand, someone still needs to wield it. Researchers are the best prepared for this.

> Bad: 'mathematics is a human enterprise + it disturbs existing incentive structures'. Mathematics is a not a human endeavor per se. It is definitely so within academia, but science is free for all. If AI can make math progress faster, then it is only for good of mathematics. It definitely does disturb existing incentive structures (grants, who proves what first, peer review), but these are not optimal to begin with and it's a good time to rethink it.

Academic mathematicians in the last 50 years have started thinking that mathematics is done solely by university-affiliated academics. This was true for around the last 100 years, but wasn't true before, and it seems won't be true for long.

And this is a good change. Good for science, good for mathematics, but perhaps bad for existing academics within their status quo incentives. But they will adapt, and mathematics will only flourish more.

In the end the goal should be to expand mathematics (and generally science) as vastly as possible. Abundance of proofs, abundance of explanations, thanks to LLMs, is a great thing for progress.

[Thomas Bloom @thomasfbloom]

@AlejandroZarUrd But it is good to have a word that specifically refers to the activity as done and understood by humans, and it seems easiest to use the word 'mathematics' to refer to this.

[Thomas Bloom @thomasfbloom]

@AlejandroZarUrd As a human, I am not ashamed to have a bias in favour of humans, and would like humans to create things to benefit humans.

AIs, or alien species, are surely capable of doing things relating to mathematics, including things that are beyond us.

[Thomas Bloom @thomasfbloom]

@JohnThilen I think there are lots of possibilities. E.g. they will start working with definitions that are simply too complicated for us to hold in our in our working memories, which are much smaller than theirs.

[Thomas Bloom @thomasfbloom]

@JohnThilen Why? The way machines understand things can be completely different from how humans understand things.

I am not saying this is necessarily going to happen (current LLMs do a surprisingly good job of explaining maths to humans!) but it is a possibility.

[Thomas Bloom @thomasfbloom]

@prz_chojecki it's good to have a measured counterpoint, and to be a voice of restraint and caution, so that we don't throw away what was good about the current system.

[Thomas Bloom @thomasfbloom]

@prz_chojecki I agree the answer is not 'keep the status quo' but it is also not 'throw away all existing institutions and structures and invent something ad hoc'.

Like most things, the best path is somewhere in the middle. And when so much of the coverage is a breathless focus on the new,

[Thomas Bloom @thomasfbloom]

@formaliser_dude Yes, that is also my belief, based on the current models of AI. But there are other forms of AI, perhaps more capable of innovation, that may come to fruition soon, and we should be prepared for anything.

[Thomas Bloom @thomasfbloom]

@Konrad_LV It is true that it is trying to protect the job of being a mathematician, and to make sure that the role of the human is still valued, and therefore people should be rewarded for doing it (as long as conventional jobs are a thing generally, anyway).

[Thomas Bloom @thomasfbloom]

@Konrad_LV I don't read it that way. Everyone can be a mathematician, and is able to read these proofs and think about them if they want.

Just like there is no special switch that makes you a programmer. If you program, you are a programmer.

If you do maths, you are a mathematician.

[Thomas Bloom @thomasfbloom]

I am not saying this is inevitable, or even likely or possible. Just that we should try our best, as early as possible, to make sure that AI and humans are aligned on what 'good mathematics' means, both abstractly and in its impact on society.

[Thomas Bloom @thomasfbloom]

But maybe there were other proofs of RH possible. Proofs that better fit our own human intuition and perspective. But maybe the AI prefers another way, and once it is done, the desire to find a human proof for ourselves will fade.