If truth in math is assumed and doesn’t require experimental evidence, then can mathematicians trust their results at all?
How I got this question:
There are assumed rules in math such as all triangles totalling 180 degrees, but without checking each triangle in the world this can never be known. Many equations are solved based on this knowledge, you are given two angles in a triangle it is easy to calculate the final angle by adding the value of those angles and subtracting by 180. I wonder if there is a single triangle in the world that doesn’t follow this rule, and if this is the case, then how will mathematicians know which one it is, and whether their answer is accurate.