Geometry is everything

Or, rather, everything is geometry.  Quantum physics and relativity are expressions of geometry.  The reduced Planck constant is the radius of a circle, or the amplitude of a photon.  The Planck constant is the circumference of a circle with the same radius, and is the momentum of a photon.  In Newtonian physics, the energy of an object would be proportional to the volume of the circle with this circumference.  (For the special case of a photon, imagine the circle lying entirely on the imaginary plane, orthogonal (perpendicular) to the real number line.  We only experience real-number events, so the photon has no energy, only momentum.)

Geometry is simple.  Calculating geometry with numbers and formulas is hard.  The simplest form of calculation is trigonometry.  Trigonometry is well understood, especially for flat (Euclidian) space.  Euclidian space is what you learned in high school geometry.  It's the space where parallel lines never meet.

It's when you go beyond simple Euclidian geometry that things get not only weird, but difficult.  General relativity is the application of the conservation of both momentum and energy to a curved space-time.  Sounds simple when you say it like that, right?  It is, until you start trying to work out how to do the math.  This was why Einstein was a genius.  He not only came up with the theory, he actually worked out the math.  He had to reinvent some of the math, because in his day, non-Euclidian geometry wasn't universally taught.

Speaking of which:  Why in the world isn't linear algebra explicitly taught as a freshman college course?  It could be taught in high school, for crying out loud.  A firm grounding in vectors and matrix manipulation would be an incredible help as a prerequisite to physics.  This is a major failing of the educational process.