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

Re:“Math 2.0” will need to value mathematical progress more ... by nicebyte on Thursday October 08, 2026 @12:06PM (#50007568)

I think we disagree pretty fundamentally on what something "being true" means.

It's possible to come up with an "unnecessarily complex model" for why someone accused of a crime did the crime, but that has completely no bearing on whether the defendant is actually guilty. If the defendant is, in fact, innocent, then the prosecution's model is, in fact, untrue - no matter how well it fits the evidence.

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Re:“Math 2.0” will need to value mathematical progress more ... by __MatrixMan__ on Thursday October 08, 2026 @12:55PM (#50008363)

> no matter how well it fits the evidence

Are you proposing that an explanation can be true even though there's a different explanation which better fits the evidence?

Or are we talking about cases where both candidate explanations fit the evidence equally, and you have access to some kind of intuition which tells you which of the two are true?

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Re:“Math 2.0” will need to value mathematical progress more ... by thaumasiotes on Thursday October 08, 2026 @08:36PM (#50014475)

> Are you proposing that an explanation can be true even though there's a different explanation which better fits the evidence?

Such a proposition would be correct; compare the concept (and name!) of "overfitting" in statistics.

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Re:“Math 2.0” will need to value mathematical progress more ... by nicebyte on Thursday October 08, 2026 @08:55PM (#50014636)

I'm talking about a case where the _best explanation_ you have suggests the defendant is guilty, however the _actual truth_ happens to be that they're innocent

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