[jimsimmons]

You don’t know who I am yet you assume I’m unable to read math. I’ll ga have you know I’ve published original proofs and derived efficient algorithms from doing very delicate math. I’m employed to do this which is something most math graduates can’t say.

I’m not advocating for dumbing down —- rather the exact opposite. People have superficial understanding of things and think they know the subject deeply because they can write a bunch of symbols. But wannabe proofs written by such people lack predictive power or explanatory value. Logic, sets and numbers are precise about the things they address just like a board game can be precise about it’s rules and outcomes. This is not the case for mathematics at large. Doing exercises in the textbook will be unambiguous because the content of the textbook grounds the meaning of objects well enough using verbose natural language. The problems are also small in size. However there is a difference between reading a law textbook vs reading the constitution. Definitions and semantics at the frontiers of mathematics are under flux and consensus among mathematicians is slow. Proofs are large and contain a lot of holes. Without the kind of verbose grounding you have in textbooks, meaning can be quite ambiguous. What is a set by the way? Since it’s a fundamental construct, can you define it unambiguously? Again I’m not asking for the notation of a set. But rather the definition of it. If you were asked to present it to a tribal person with no formal education, do you think the definition you thought of would have the same explanatory value to them? If this constraint made you rethink your definition you see my point.

I’m not talking about any creative aspect. I’m just talking about formalisation. Geometry is notoriously hard to formalise for computers. Take a look at the Lean theorem prover and how hard it has been to formulate large sections of math despite repeated attempts over decades. The creativity you suggest is actually rooted in the pattern processing machine that is the brain which fills in large blanks left out from formal representation and which many mathematicians take for granted without realising the extent of ambiguity it brings.

Your language and usage of R word suggests you’re in an Ivory tower just because you understood a few problems in your textbook at some point.

[simion314]

Can you just give me an example? Like link to your work or someone else(preferably a mathematician) that does rigorous proofs using natural language. Maybe i do not understand exactly your point, you want some symbols so what is the rule what symbols are allowed and what not.

Not sure what you mean about defining a set, as I mentioned in Math fundamentals you have no choice then to define a few initial primary terms and axioms to bootstrap things.