The 'cheat code' approach to math results, a result which no one understands, and which no one can teach has no real value.
The system of payment for publications in order to support math discovery is simply the narrow 'commercial system' applied to supporting foundational science in the absence of a broader civilization level appreciation for the mathematical arts. Looking to history, from the late renaissance through the early 20th century the support for mathematical discovery was more generally understood and supported by institutional level organizations and more generally understood to be important for the progress of scientific progress by the private and public wealth .
This system enabled the development of topology, numerical analysis, complexity, set and group theories. The lapse in this level of support that did not give mathematicians the same protection from front line deployment in WWI brought that era to nearly a close. Reading about 'Nicholas Bourbaki' might lend some deeper appreciation of the effects of the losses from that shift in collective appreciation of foundational math.
The idea that these LLM's are getting results that mathematicians haven't produced demonstrates the shallow understanding of math in modern times, due in part to the limited accessibility of so much of the prior writings of the entire history in mathematics, whether that be due to few surviving copies of some arcane work in a private library collection, or due to a modern fee for access paywall. One example of this condition can be shown with a small excerpt from a work that I am currently composing:
"In 1805, while computing the orbits of the newly discovered asteroids Ceres, Pallas, and Juno from limited observational data, Gauss developed an efficient method for evaluating trigonometric interpolations by recursively decomposing large sums into smaller ones before recombining the results. Because of a steadfast adherence to Gauss' own personal motto, "Pauca sed matura" (Few, but ripe), Gauss never formally published this specific algorithm nor the conclusions of investigations which also laid the foundations of non-Euclidean geometry. These methods remained hidden in his notes under a manuscript titled Theoria Interpolationis Methodo Nova Tractata which was published in 1866, 11 years after his death, and the Fast Fourier Transform-equivalent approach within it remained largely unnoticed until the twentieth century, when James Cooley and John Tukey independently rediscovered the same computational strategy. His discovery was seventeen years before Joseph Fourier published the original Fourier Transform in his 1822 results on harmonic analysis."
That is to say; Tukey and Cooley were unaware when they discovered FFT that the knowledge had lay hidden in an obscure work for centuries. It should be understood that these 'novel' LLM discoveries are simply the models traversal of the huge corpus of all the maths publications in the training set, collecting and rearranging these techniques into synthetic 'results'. They are attention getting, but they are not new, and the proofs are insufficient to the task of improving the utility of mathematics for humanity.
The 'disgruntled mathematicians' aren't selling anything. They are informing civilization as a whole that having a cheat sheet to the math test only cheats yourself in the end, the same point that math teachers have been making since grade-school. Anyone who doesn't internalize that truth will always need someone else to do the math for them.
To paraphrase Curtis Jackson, ""If you don't know the numbers, you don't know your business."