nprofile1qyt8wumn8ghj7un9d3shjtnyd968gmewwp6kytcqypren5k53ms4x26agn2qg4anqpe3a7zuy39qjjd5slavzskqn2qgxcaztfm (nprofile…ztfm) As a counterpoint, I have a belief (which is hard to substantiate with more than anecdotal facts) that if "generic mathematics" mostly doesn't run into independence phenomena, it is also because "generic mathematicians" more or less consciously *stay clear* of independent statements and more generally anything that requires them to think about foundations, a topic that makes them uneasy.
(Relatedly, I have noticed many times how mathematicians, who usually talk about mathematics with great precision and clarity of thinking, strangely switch to hearsay, vagueness and weasel words as soon as logic is involved.)