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We have grown accustomed to being ‘subjected to’ scientific progress as if it were a triumphal and unstoppable march. We live surrounded by a pervasive technology that grants us the illusion of an ever-deepening knowledge of reality. Yet, if we look at the foundations of theoretical physics, the landscape that appears is one of a desolate epistemological stagnation.
For over fifty years, fundamental physics has failed to produce a true ontological revolution. We have confirmed theories born in the last century—such as the Higgs boson from the 1960s or Einstein’s gravitational waves from the beginning of the century, the only two true demonstrations of fundamental theories in recent decades—but we have not given birth to a single new idea that has been proven real (see What’s wrong with scientific research according to Sabine Hossenfelder). On the contrary, we have retreated into a sort of ‘maintenance of paradigms’ (in the Kuhnian sense), adding mathematical patches to models that no longer function (see Kuhn’s “The Structure of Scientific Revolutions” in a nutshell).

The Trap of the ‘Millennium Problem’

A perfect example of this drift is the celebrated Millennium Problem regarding the Navier-Stokes equations (see A pure mathematical version of the Clay Mathematics Institute’s Navier-Stokes Millennium Problem). We are asked to prove whether a ‘smooth’ (continuous) solution can explode into a mathematical singularity. But who does this research truly benefit?
There is a certain arrogance in demanding that the mathematics of the absolute continuum—a tool invented three hundred years ago—must be the faithful mirror of a reality we know to be intrinsically granular. Seeking regularity or singularity in Navier-Stokes is an exercise in the internal consistency of an axiomatic system, a ‘mathematical little game’ that adds nothing to our understanding of matter.
It is a restaging of the late 19th-century ultraviolet catastrophe: classical physics predicted the emission of infinite energy from a black body because it assumed energy was infinitely divisible. Max Planck did not ‘solve’ the calculation problem that diverged; he changed the logic, introducing the quantum of energy—a granular discretization (see Planck’s photon distribution function). Today, persisting in the search for regularity in continuous fluid dynamic models without accepting the logical (and physical) limits of that language is like trying to measure an atom with a ruler: the error is not in the mathematical calculation, but in the model adopted.

The Ptolemaic universe of dark matter

If Navier-Stokes is a dead end for brilliant minds, modern cosmology has become a triumph of epicycles. Kuhn taught us sixty years ago that when a paradigm enters a crisis, the scientific community does not abandon it immediately, but instead begins to ‘save’ it with ‘ad hoc’ hypotheses.
Thus, to make General Relativity equations square with a universe that moves differently than predicted, dark matter and dark energy were invented. We do not see them, we do not know what they are, and we do not understand their nature. They are ‘magical patches’ necessary to prop up models that we are unable to interpret. We are planning trips to Mars using a modernized Ptolemaic system, convinced that adding an invisible epicycle is nobler than admitting we have failed to understand the nature of gravity on a large scale (see Note for laymen – what is the dark matter?).

The Deception of Technological Progress

The common objection is: “How can you speak of stagnation when Artificial Intelligence and silicon dominate the world?”
Here lies the fundamental misunderstanding. Technology is not fundamental science; it is the exploitation of past discoveries. Computers are based on the quantum mechanics of the 1920s and 30s; our rockets on 19th-century thermodynamics. Technology is the engineering that refines the already known, but the theory upon which it is founded remains old—tremendously old. We are utilizing maps that ignore 95% of the territory, or that are incapable of observing it in its true reality.

The Tyranny of the ‘Barons’ and the veto of the paradigm

Why do we not move forward? Because knowledge has become a hostage to a feudal academic structure. The ‘Barons’ of the paradigm are slaves to their own careers and the consensus of the community. Risk is not funded. Anyone proposing a sensible cosmological model that does not include invisible ‘ghosts’ is isolated, denied publication, and stripped of funding.
The system prefers to distract superior minds by challenging them with inessential problems—like Navier-Stokes singularities or calculating the galactic halos of magical components—rather than facing the terrifying uncertainty of a paradigm shift. We are moving backward, not forward, because we have lost the ability to see the problem before calculating the solution.

Conclusion: seeing beyond the fence

Mathematics is indifferent to the survival of the solution, but we should not be. The task of research is not to balance the books of a useless abstraction, but to find the correct language to describe reality.
The result regarding the Navier-Stokes singularity will not change the empirical efficacy of the laws of dynamics. It would perhaps establish (with due respect to Gödel) whether the continuous model is a coherent language or if it is destined to succumb to its own abstraction.
The true challenge is having the courage to admit that our reference models do not describe reality, and that it is necessary to explore new descriptions of nature beyond a “déjà vu that simply ‘does not work’ (by the very admission of those who continue to support it).
While waiting for a visionary genius to find a better description of reality, we could, in the meantime, make room for the visionaries who see beyond the fence…