Mathematics as an Information Process

 ... or "how any brains, human or artificial, can do maths" : including the creation of novel concepts for nouns, verbs, and adjectives in maths.

I started writing this as a comment on Valerio's post, but it overflowed so I made it a repost, then it overflowed, so I had to articleise it.

What the hell is maths?

I think categorically, "mathematics" isn't "a thing that can be solved" as a whole. Mathematical QUESTIONS yes, but there is no end to the questions.

Mathematics ITSELF is a [ software program ], for [ representing ways to reason about phenomenology in general ] - in other words, maths is a programming language, or compiler toolchain - with specific focus on [ phenomenology that is objective ].

( This applies to mathematics as a social activity - in private, any mind can perform subjective quantification upon phenomena it perceives, even though that activity is not directly observable by other minds. Because at this point in history, we still do not have [ social / common access ] to the [ subjective phenomenological experience of humans ], since that memory space is embedded within an ill-understood meat net. )

I think the matter of coming up with new [ mathematics, and science in general ] is really just a generative process of creating ontologies of language where existing ontologies are insufficient. It's just mutate, and cull, loop. What gives rise to the DEMAND for new ontology / concepts, depends a bit more on the field.

PHYSICS :

In physics, ontological DEMAND is a matter of "we have some observational SENSORY data that does a quantifiable pattern, but we don't have a name for the pattern, though we can point at the pattern. Also we don't know how this new pattern relates to old patterns, and we need to do more tests to find out."

MATHEMATICS :

In mathematics, ontological DEMAND is a matter of "basically everything that physicists do, but swap the object of research from SENSORY phenomena in general to [ formal INSENSIBLE verbal concepts, attached to some SENSIBLE notation that we use to represent it ]".

THE DIFFERENCES :

While physicists have to tolerate the limit of "hypotheses are falsifiable, and resistant to falsification under duress," mathematicians tend to need to show that "theses are necessarily true/false".

In the realm of testing the combinatorial play-niceness of known fundamental relations and entities, that's fairly straightforward.

THE COMMONALITIES :

The discovery of new fundamental relations and entities ... is also driven, from the same sensory source that drives such discovery in physics.

Physics and mathematics are both "sensory", it's just that in physics the sensory data is of [ intrinsic ] interest, whereas in maths the sensory data is [ just symbolic of insensible interests ].

So, in the same way machines can be programmed to be creative in hypotheses about [ intrinsically interesting sensory data ], they can do the same for [ sensory data, i.e. language morphemes and syntax, which are extrinsically interesting ].

THE MENTAL MODAL :

After all, in and of itself, [ the latent intuition about how logic, space, and time, work ] is essentially the brain's physical activity, as a [ subconscious memory space ]. Data from there then intrudes, from time to time, upon our also physical [ imaginations, as conscious memory spaces ].

Both memory spaces simply process [ sensory data structures, which we may call qualia when they move into the conscious memory space ].

A practiced thinker knows how to completely map, FROM qualia, TO analogous signals or other data structures which are known to be objectively quantifiable, through the social practice of science.

Of course, I might be venturing a bit too far here, in terms of asserting that meat brains are just sub/conscious physical information processes.

Haha