While the title does sound a bit sensationalist the actual paper refers to a standard in the International Commission for Weights and Measures which is indeed (according to the paper) based on 100-year old paradigm introduced by Riemann and furthered by Helmholtz and Schrodinger.
From the abstract:
The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz and Schrödinger, that perceived color space is not Euclidean but rather, a three-dimensional Riemannian space. We show that the principle of diminishing returns applies to human color perception. This means that large color differences cannot be derived by adding a series of small steps, and therefore, perceptual color space cannot be described by a Riemannian geometry.
This makes sense to me. As I've said elsewhere below, the eye adapts dynamically to each situation. One's perception - the dynamic range of both color and luminance is situational and adaptive.
I know from personal experience of being fooled on hundreds occasions when trying to judge colors, color temperature, etc. despite my experience and the fact that my color vision is normal (I've never failed any Ishihara or related tests).
The law of diminishing returns is essentially what I experience as an observer, the more I grind my observation fine the more fooled and less objective I become. I now only believe my instruments.
Thus it makes sense that large color differences cannot be derived by adding a series of small steps simply for the reason they are in effect a form of noise in relation to large steps.
"therefore, perceptual color space cannot be described by a Riemannian geometry."
Perhaps Riemannian geometry should become just a starting point if for no other reason than it serves to illustrate the complexity of human color perception and the difficulty it poses in trying to analyze it.
From the abstract:
The scientific community generally agrees on the theory, introduced by Riemann and furthered by Helmholtz and Schrödinger, that perceived color space is not Euclidean but rather, a three-dimensional Riemannian space. We show that the principle of diminishing returns applies to human color perception. This means that large color differences cannot be derived by adding a series of small steps, and therefore, perceptual color space cannot be described by a Riemannian geometry.
https://www.pnas.org/doi/10.1073/pnas.2119753119