About math limitations
“Mathematics is limited by the physics because physics constrains our brains” only works if you hold the philosophical view of physicalism. People who hold that view believe that the current physical model of reality is all there is and the utmost absolute truth.<p>Materialistic monism is a popular but not particularly robust view in my opinion, because those models can never be complete and always evolve in directions guided by the applications and predictions our minds seek. (Other views are available.)<p>I would encourage more people to apply the same principle at the higher level, changing “our brains are limited by physics, hence our mathematics is limited by physics” to “our model of reality, <i>including physics,</i> is limited due to our minds operating within that reality”. In other words, the model that makes you think your consciousness comes from neurones and is thus limited by physics is itself a product of your consciousness, and conclusions you make based on that model (such as “mathematics is limited by physics”) should be taken with a grain of salt (not just as possibly wrong but, worse, not-even-wrong) because you can’t construct a complete model of a system from within said system.<p>But the kicker is that this logic itself is rooted in mathematical reasoning (see Gödel’s incompleteness theorem), so take it for what you will.