# Mathematically rigorous introduction to color theory? (Reference request)

I am looking for an introduction to color theory that presupposes knowledge of considerable mathematics and physics. Such a theory should carefully address how a light spectrum, which can be fully represented as a Fourier transform of a signal in $$L_2(\mathbb R),$$ can be well approximated by a point in some sort of color space, e.g., LMS or RGB.

Essentially, I would like a reference that introduces the topics discussed in this question, geared at someone with a background in math and physics but not color theory.

EDIT: To give a sense of what I mean by the math/physics side of color theory, I'm interested in the following types of question:

What is the definition of the chromaticity diagram?

How come three pixels can produce all the colors in the convex hull of those pixel's representative points on the chromaticity diagram?

How does RGB space map onto the chromaticity diagram? (The pixel for $$(R,G,B)=(1,0,0)$$ should map to the "red" vertex of a triangle, but how about the point $$(R,G,B)=(0,0,0)?$$)

Why are most colors on the chromaticity diagram not producible from pure frequencies? Why do all the pure frequencies form one boundary for the chromaticity diagram, while the violet-red boundary line can only be produced from mixture of frequencies?

• Jeez, are you really sure rigorous math is the right way to approach this subject? Sure, you can use fancy math in the most basic, trivial first step (of taking a Fourier transform). Everything after that is all about biomechanics, chemistry, and neuroscience, and can't be productively formalized to the same degree. Commented Jun 7, 2021 at 17:21
• @knzhou I'm interested in things like: the definition of the chromaticity diagram; why the convex hull of three points on it is producible from three pixels made of those points; how RGB space maps onto it; why most colors on it are not producible from pure frequencies. Commented Jun 7, 2021 at 18:10
• So less about the biophysics, chemistry, and neuroscience side, and more the physics/math side. In fact, the hard part of finding resources on this subject is that it's hard filter out all the biophysics/chem/neuro stuff to find what I'm really looking for. Commented Jun 7, 2021 at 18:12
• Edited the post with the hope of clarifying this distinction. Commented Jun 7, 2021 at 18:23