Is the system of Mathematics derivative from the corporeal nature of experience?

Question

I do not consider myself religious, but I have come to know Mathematics as my way of looking at the universe. I seem to have come to the (premature?) conclusion that it is the most developed way we have to explore the semantic contents of our universe without need of sensory input. Recently though, I have begun questioning whether or not that is actually possible.

Does a system such as Mathematics, inasmuch as a heuristic for developing formal systems in a rigorous manner by way of axiomatic construction, rely on sensory experience for the conclusions we draw? Furthermore, would it even be possible for a living person who had never experienced sensation to have thoughts and explore the internal nature of their own minds? Would they ever be able to conjecture about the "outside" world?

The only possible way I can think of so far is that a sensory mute would have to learn what language was internally. They would still be equipped with all of the necessary cortexes in their brain for producing such feedback, so perhaps they could create a language based upon controlled hallucination. I still don't know whether or not their thoughts would resemble our own though, and I feel without a neuropsychological approach it would be very hard to discern the answer.

Does anyone know of research that has been done in this area?

Answer 1

For research in this field see for instance :

Spät, Knaup, Müller (eds.): Post-Physikalismus, Herder (2014): The keyword is Hylemorphism.

Röd, Poggi: Die Philosophie der Neuzeit, Band 4, Beck (1989) p. 265: "L.G.A. de Bonald: So wie es keine Erkenntnis ohne Sinneseindrücke, Empfindungen und Raisonnement geben kann ..."

Allerkamp, Mirbach: ‎Philosophy (2016): "Menschliche Erkenntnis, die gemäß sensualistischer Vorgaben ohne Sinneseindrücke nicht auskommt ..."

The sources are in German. The essence is this: Without any sensual experience you would not have any basis for thinking. What do you need to think 1 + 1 = 2? Two apples or two strokes or two clouds? You need something: pictures, letters, sounds. Even Helen Keller could add two bodily contacts or count her heart beat.

Like writing is impossible without letters, like space is impossible without matter or energy, thinking is impossible without the memory of sensual impressions.

Mathematics is impossible without reality in two respects: You need reality to abstract the mathematical notions from it. And you need reality to think and to express the results of our thinking.