I am reading historical stuff on the algebraic and transcendental numbers. Descartes, in his Geometry, excluded all curves not expressible as algebraic equations. Later, Leibniz called such curves transcendental.
I wonder now which automata recognise exactly the algebraic numbers? As Turing showed, Turing machines can recognise all algebraic numbers. Apparently, finite state machines cannot recognise algebraic numbers. So, there must be an automata class between that does the job?