Temperature and heat are examples from physics which I considered using for the post, though they didn’t end up in there. Force, pressure, mass, density, position/velocity/acceleration, charge and current, length, angle… basically anything with standard units and measurement instruments. At some time in the past, all of those things were just vague intuitions. Eventually we found extremely robust mathematical and operational formulations for them, including instruments to measure those intuitive concepts.
On the more purely mathematical side, there’s numbers (both discrete and continuous), continuity, vectors and dimensionality, equilibrium, probability, causality, functions, factorization (in the category theory sense), lagrange multipliers, etc. Again, all of those things were once just vague intuitions, but eventually we found extremely robust mathematical formulations for those intuitive concepts. (Note: for some of those, like lagrange multipliers or factorization, it is non-obvious that most humans do in fact have the relevant intuition, because even many people who have had some exposure to the math have not realized which intuitions it corresponds to.)
Temperature and heat are examples from physics which I considered using for the post, though they didn’t end up in there. Force, pressure, mass, density, position/velocity/acceleration, charge and current, length, angle… basically anything with standard units and measurement instruments. At some time in the past, all of those things were just vague intuitions. Eventually we found extremely robust mathematical and operational formulations for them, including instruments to measure those intuitive concepts.
On the more purely mathematical side, there’s numbers (both discrete and continuous), continuity, vectors and dimensionality, equilibrium, probability, causality, functions, factorization (in the category theory sense), lagrange multipliers, etc. Again, all of those things were once just vague intuitions, but eventually we found extremely robust mathematical formulations for those intuitive concepts. (Note: for some of those, like lagrange multipliers or factorization, it is non-obvious that most humans do in fact have the relevant intuition, because even many people who have had some exposure to the math have not realized which intuitions it corresponds to.)