What is it like to have an understanding of very advanced mathematics?
You can answer many seemingly difficult questions quickly. But you are not very impressed by what can look like magic, because you know the trick. The trick is that your brain can quickly decide if question is answerable by one of a small number of powerful general purpose “machines” (e.g. continuity arguments, combinatorial arguments, correspondence between geometric and algebraic objects, linear algebra, compactness arguments that reduce the infinite to the finite, dynamical systems, etc.).
One of a long list.
It’s hard to convince those that don’t “speak” math how necessary it is, rather than being forced to explain things in a much less precise language (be it English or something else) that the audience understands.
via @seanmcarroll
If math were both necessary and sufficient, then economics, quantum gravitations, and SUSY would work. Mathematics, by definition, is not empirical. Euclid made no mistakes. Euclid is fine on a flat plane or a cylinder’s surface. Euclid on a torus, ellipsoid, or nuclear power plant cooling tower is terrifically wrong.
The Shroud of Turn is the projection of an ellipsoidal face upon a planar cloth without distortion, cuts, or tucks. That anybody would argue in support of its authenticity, given the maths, is astounding. Oh yeah, “test of faith!” Math as such cannot convince faith.
Make Shrouds of Turin at will with a bas relief full face sculpture (template), a kitchen oven (rather less than 230 C template temp), and a heavy cotton cloth (white denim). Galileo recognized the power of empirical reality. Faith cannot survive being ridiculous.
http://wwwdelivery.superstock.com/WI/223/1606/PreviewComp/SuperStock_1606-78238.jpg
Shroud of Buddha template.