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## How would a philosopher of math describe what happened when ancient

How would a philosopher of math describe what happened when ancient mathematicians discovered (?) the number zero?

I think the answer will depend on which philosopher of math you ask. As you seem to recognize, some philosophers of math deny that numbers exist independently of us in such a way that their existence is genuinely discovered by us. Even philosophers of math who think that numbers are discovered might say that your question -- "What happened?" -- is an empirical historical or psychological question rather than a philosophical one. In any case, you'll find relevant material in the SEP entry on "Philosophy of Mathematics" at this link.

Ancient mathematicians (Babylonian, Egyptian, Greek) did not in fact discover the number zero. The discovery is thought to have been in India, which was the first place to treat zero like any other number (rather than as a placeholder), sometime between the 6th and the 10th century CE. It is thought that this advance required abstract thinking that was perhaps facilitated by Indian Philosophy. The discovery spread to the West through Arabic mathematics.

## I am often confused by the rhetorics of physicists that their theory "came from

I am often confused by the rhetorics of physicists that their theory "came from mathematics". I remember the physicist, Brian greence tell the story of paul dirac discovery of anti-matter by pure a priori manipulation of mathematics. I see this to be very confusing, because i often imagine mathematics as being a priori, and necessary without any connection to the real world. That is, i can always imagine possible worlds( or universes) governed by different mathematical expressions, or descriptions. Does it follow that every mathematical expression/description describes our universe? Obviously not. With paper, and pencil, we could probable describe any universe with any arbitrary number of dimension of space, but does it follow that our universe has arbitrary number of spatial dimension? Obviously not. The use of mathematics seems to be good in formulating regularities of nature( laws of nature), and to extract the implication of those laws. It makes me wonder why physicists would say their theory comes...

You are reasoning correctly--mathematics deals with possibilities and physics with actualities (even though in quantum mechanics these are probabilistic). Theory in physics is often expressed mathematically, but that does not make it mathematical knowledge. Some theoretical advances in physics can come from working in an armchair and extending the mathematical implications of (already accepted and contingently true) theory. The actual status of mathematics (a priori or not) is debatable (Quine etc claiming that mathematics is an empirical theory like any other). But you are correct that physics is not mathematics, and the sort of evidence that confirms physical theory is not (or perhaps, not entirely) the evidence (or other considerations) needed to confirm mathematics.

You are reasoning correctly--mathematics deals with possibilities and physics with actualities (even though in quantum mechanics these are probabilistic). Theory in physics is often expressed mathematically, but that does not make it mathematical knowledge. Some theoretical advances in physics can come from working in an armchair and extending the mathematical implications of (already accepted and contingently true) theory. The actual status of mathematics (a priori or not) is debatable (Quine etc claiming that mathematics is an empirical theory like any other). But you are correct that physics is not mathematics, and the sort of evidence that confirms physical theory is not (or perhaps, not entirely) the evidence (or other considerations) needed to confirm mathematics.