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EDIT: I THINK I STAND CORRECTED
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There is, though. Maybe not wide in your inner circle, but very, very wide if you actually look around.
Ex-mathematician here, almost certainly in a different "circle," no there isn't. There are widely accepted standard definitions of things like integer, rational, real or complex number. But "number" is not really well defined. Frege's Foundations of Arithmetic contains a classical exploration of this exact question if you'd like some perspective.
How can you be an ex-mathematician? Maybe is a language barrier (English is not my main language), but I thought that was a designation based on your knowledge.
Mathematician is a professional title. I quit the profession and now work as a software developer.
Ah, got it. Thank you for the clarification!