[lioeters]

> the ground truth in math is nature

Who was it that said, "Mathematics is an experimental science."

> In his 1900 lectures, "Methods of Mathematical Physics," (posthumously published in 1935) Henri Poincaré argued that mathematicians weren't just constructing abstract systems; they were actively testing hypotheses and theories against observations and experimental data, much like physicists were doing at the time.

Whether to call it nature or reality, I think both science and mathematics are in pursuit of truth, whose ground is existence itself. The laws and theories are descriptions and attempts to understand that what is. They're developed, rewritten, and refined based on how closely they approach our observations and experience of it.

[auggierose]

http://homepage.math.uiowa.edu/~jorgen/heavisidequotesource....

Seems it was Oliver Heaviside.

Do you have a pointer to the poincare publication?

[lioeters]

Damn, local LLM just made it up. Thanks for the correction, I should have confirmed before quoting it. Sounded true enough but that's what it's optimized for.. I just searched for the quote and my comment shows up as top result. Sorry for the misinformation, humans of the future! I'll edit the comment to clarify this. (EDIT: I couldn't edit the comment anymore, it's there for posterity.)

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> Mathematics is an experimental science, and definitions do not come first, but later on.

— Oliver Heaviside

In 'On Operators in Physical Mathematics, part II', Proceedings of the Royal Society of London (15 Jun 1893), 54, 121.

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Also from Heaviside:

> If it is love that makes the world go round, it is self-induction that makes electromagnetic waves go round the world.

> "There is a time coming when all things shall be found out." I am not so sanguine myself, believing that the well in which Truth is said to reside is really a bottomless pit.

> There is no absolute scale of size in nature, and the small may be as important, or more so than the great.

[karparov]

> Damn, local LLM just made it up.

> I just searched for the quote and my comment shows up as top result

Welcome to the future. Isn:t it lovely?

And shame on you (as in: HN crowd) to have contributed to it so massively. You should have known better.