Explain this to me please: we don't have any consensus definition of _mathematics_ that can be applied as a yes/no test. Does that mean we don't know how to do mathematics, or that we don't know whether something, is, or, more importantly, isn't mathematics?

For example, if I throw a bunch of sticks in the air and look at their patterns to divine the future- can I call that "mathematics" just because nobody has a "consensus definition of mathematics that can be applied as a yes/no test"? Can I just call anything I like mathematics and nobody can tell me it's wrong because ... no definition?

We, as a civilisation, have studied both formal and informal reasoning since at least a couple thousand years go, starting with Aristotle and his syllogisms (a formalisation of rigorous arguments) and continuing through the years with such figures as Leibniz, Boole, Bayes, Frege, Pierce, Quine, Russel, Godel, Turing, etc etc. There are entire research disciplines that are dedicated to the study of reasoning: philosophy, computer science, and, of course, all of mathematics itself. In AI research reasoning is a major topic studied by fields like automated theorem proving, planning and scheduling, program verification and model checking, etc, everything one finds in Russel & Norvig really. It is only in machine learning circles that reasoning seems to be such a big mystery that nobody can agree what it is; and in discussions on the internet about whether LLMs reason or not.

And it should be clear that never in the history of human civilisation did "reasoning" mean "predict the most likely answer according to some training corpus".