Mathematics does not need axioms and does not need verbalized proofs.
Applied mathematics answers questions like: if I have 3 apples and get 2 apples, how many apples do I have? 3A + 2A = 5A is a theorem. It can be proved and has been proved by simply doing the experiment. (Mathematics is physics where the experiments are cheap (V.I. Arnold).) No axioms are required.
Same holds for calculating the contents of granaries. Since mathematics is abstracted from reality it can best be checked by reality which is a better computer than all human productions of that kind.
In general axioms only are introduced to show post festum that also useful mathematics can be formalized. But mathematics without axioms is not of less value than the Greek mathematics and it has been pursued for thousands of years by Egypts and Babylonians in a much more sophisticated way than by the Greek.
The Egypts were the first to solve a quadratic equation. That is mathematics, if the solution is correct as can be proved by doing a suitable experiment. Further proof is not required.
For the high level of ancient Egyptian mathematics see https://en.wikipedia.org/wiki/Ancient_Egyptian_mathematics .