"This is unacceptable because mathematics is written as English is written in complete, grammatical sentences." Unfortunately natural languages have many flaws

"This is unacceptable because mathematics is written as English is written in complete, grammatical sentences." Unfortunately natural languages have many flaws and will easily falls in contradiction like Russell's paradox. Even formal mathematical axiomatic systems encountered Gödel's incompleteness.. Maybe something like constructive category theory would give us a better way to formally put ideas in ...