1. Do the angles of a triangle always add up to π radians? Although this is the case in Euclidean geometries, where the shortest path between two points is the straight line joining them, there are geometries for which this is not so.  Imagine the earth to be a perfect sphere and consider the spherical triangle formed by the North Pole, and any two points on the equator that have perpendicular meridians. The sum of the angles of this triangle is 1.5π radians.  In fact, the sum of the angles of a triangle on the unit sphere is π plus the area of the triangle. 

2. Where do numbers come from? Do numbers exist out there somewhere and are real entities, or are they the product of human contrivance?   Hard to say. They appear to be embedded in the world in ways that we can’t completely comprehend. They merely began as measurements of quantities and grew into the means for the most precise expressions of the physical world.  But it’s hard to believe that the Pythagorean theorem is somehow floating out there in the cosmos and is not just a regularity noticed and expressed in mathematical form by humans!