Well, we all know Euclid´s “Elements” and weird problems such as prime counting functions (see Terence Tao´s blog for this). A simple addendum to Euclid´s ideas would be to say that instead of the normal axioms (0 dimension = point, 1 dimension = line etc…) a monomial or polynomial already encodes such properties. Instead of…

If the Universe could be observed as a generalized wavefunction $psi$, perpetually collapsing unto physical properties, what axioms would hold for a coherent picture of reality? A generalized Hilbert space, following von Neumann algebras? Not very pretty. Cauchy´s integral formula and theorems are prettier: Essentially, it says that if  is holomorphic in a simply connected domain Ω, then for…

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