All mathematics is produced by physical objects (brains, computers). Therefore the laws of physics determine what theorems are possible, and mathematics has no existence independent of our universe.
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Would this not suggest that the laws of mathematics could be different for an alien species?
You don't even need alien species. We humans already have many different laws of mathematics. Check this out:https://www.youtube.com/watch?v=RlMMeqO7wOI …
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Are there any examples of how another version of mathematics might look? He talks about lots of possible alternative systems, but there's no details on how they would differ in practice.
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Good find and Wolfram is obviously a smart guy but he seems a little misguided here. It is easy to imagine a different math but that math should always be translatable to our math. Think polar vs Cartesian coordinates. Math will change to absorb all useful discoveries.
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No, the axioms may be incompatible.
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