“Math 2.0” will need to value mathematical progress more holistically

Re:“Math 2.0” will need to value mathematical progress more ... by godelski on Thursday October 08, 2026 @08:34PM (#50014457)

  > but Ptolemy and Copernicus weren't talking about mass or causality

Except they were

My critique is that there's a difference between "x is the center" and "motion looks like y when sitting at x".

Those are different claims with very different consequences. You're dismissing this as minutia but that minutia is the critical point. In a geocentric model you need to explain why things revolve around the earth. In a heliocentric model you need to explain why things move around the sun. Predicting the motion of the planets doesn't answer these. But answering these *correctly* allows you to build a generalized model in which you can predict the motion of planets, in any arbitrary system.

I'll also add that I love the geocentric model as a good illustration of why observation alone can't give you causality. There's far more to science than data fitting. In fact, that's why all the mathematicians are getting upset and what Tao has been talking about this whole time

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Re:“Math 2.0” will need to value mathematical progress more ... by __MatrixMan__ on Friday October 09, 2026 @02:51AM (#50016945)

I don't think Copernicus did any explaining why at all. That took another 150 years.

We now bind our physics to our astronomy, but they didn't then. That's what I mean by it being a matter of taste, not of truth.

If you were prompting a godlike LLM for a theory of the heavens in the 1540's you probably wouldn't have used words like "mass" at all, and the theory that it spit out would be similarly absent that concept.

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Re:“Math 2.0” will need to value mathematical progress more ... by godelski on Friday October 09, 2026 @12:05PM (#50022537)

  > I don't think Copernicus did any explaining why at all.

He did. I mean even ask yourself, why would he do what he did if he was just concerned with motion? Ptolemy's model was accurate for predicting motion. If it was just about motion, then the viewer's position doesn't matter.

But Copernicus's enables us to say more. It is more elegant (it was not simpler though). Copernicus was seeking realism. He was the person annoyed with how complex a system was while everyone around him was saying "who cares, it works".

  > That's what I mean by it being a matter of taste, not of truth.

There is no taste to truth, only taste in how you convey truth

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Re:“Math 2.0” will need to value mathematical progress more ... by __MatrixMan__ on Friday October 09, 2026 @05:40PM (#50026912)

I was taught that Copernicus's work was a more elegant predictive system: these equations work and are nicer than those, without attempting to address causation. Nothing about gravity in there. I guess I'll have to read his work and find out.

As for your second point, it seems we agree. They're orthogonal. Even if a machine can give you one, the other still needs doing.

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Re:“Math 2.0” will need to value mathematical progress more ... by godelski on Sunday October 11, 2026 @03:11PM (#50046731)

Note that Copernicus's system still has epicycles. So it was still fairly complicated. More elegant, but still complicated. It also, importantly, gives order to the planets. Distinguishablity matters

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