Well yes folks. Understand that my work has cracked open the second order barrier allowing all mathematical method to advance into all problems dealing with more than two axis.
Just what do you think third and forth order pythagoreans mean?
for a human being, the calculation load becomes unbearable because it climbs exponentially. I have already tasted it..
Yet adopting my method may also allow most mathematical inquiry to be fprmally closed. Perhaps not sll ,but that is a question to be answered.
Will Mathematics in the Age of Superintelligence Follow the History of Astronomy in the Age of Instrumentation?
Avi Loeb
Avi Loeb
The IceCube Neutrino Observatory at the South Pole is funded and managed by the U.S. National Science Foundation. In 2026, the Physics Nobel Prize was awarded to the Observatory’s Principal Investigator, Francis Halzen for the discovery of high-energy neutrinos of astrophysical origin. (Image Credit: Chris Michel/Wikimedia)
Ancient astronomy was practiced for thousands of years. For example, the Mayans used their eyes to track changes in the positions and relative brightness of the Sun, Moon, planets and stars for over 2,000 years. Mayan astronomers acquired the highest status in their society as priests who advised their rulers on major decisions about state events, marriages, and wars.
The human eye achieves an angular resolution of about an arcminute (1/60th of a degree) in the visible wavelength band between 380 and 720 nanometers. Given the limited collecting area of the pupil, 3–50 square millimeters, humans were able to see only relatively bright sources of visible light, as needed for their survival. Mayan astronomers with sharper eyes had the privilege of identifying fainter sources in the sky. Given the interest of Mayan rulers in their findings, they must have been celebrated and rewarded based on the quality of their eyesight.
Starting with Galileo Galilei in 1610, astronomers employed telescopes to observe the sky. 380 years after Galileo’s first observations, the Hubble Space Telescope (HST) was launched beyond the Earth’s atmosphere, to alleviate the compromising atmospheric glow and blur. HST features a primary mirror with a collecting area of 4.52 square meters, about 100,000 times bigger than a fully dilated human eye. Its angular resolution is 1,200 times sharper and it can detect sources that are 10 billion times fainter than what an unaided human eye can see.
Whereas early telescopes probed electromagnetic waves at the frequency range visible to the human eyes, their advanced successors probed other frequencies including the radio, infrared, ultraviolet, X-ray and gamma-ray bands. In addition, the detection of cosmic-rays, neutrinos, and gravitational waves offered new insights on otherwise invisible processes throughout the cosmos.
Are we witnessing an accelerated repeat of this history in the context of mathematics in the age of artificial superintelligence?
Traditionally, mathematicians used their biological brains to prove or disprove research conjectures. Over the past few months, advanced reasoning models from OpenAI, Anthropic, and DeepMind have generated thousands of pages of manuscripts, found counterexamples to long-standing math problems, and computerized historic human proofs. These include discovering a partial proof of the Quasi-Riemann Hypothesis and a major special case of the Hodge Conjecture, disproving long-standing conjectures such as the Köthe Conjecture, the Ibragimov–Iosifescu Conjecture, the Discrete Geometry Conjecture, the Crouzeix Conjecture, and the Erdős Unit Distance Conjecture. Superintelligence (SI) agents successfully resolved several open Erdős problems and verified dozens of integer sequence conjectures. SI labs now pair Large Language Models with interactive proof assistants like Lean. The SI acts as the creative engine, guessing lines of a proof, and Lean acts as a fact-checker, telling the SI if a step violates mathematical rules. This feedback loop allows SI agents to autonomously debug their logic until a bulletproof code certificate is produced
The use of instruments with super-human abilities to explore mathematical truths resembles the use of astronomical instruments to explore invisible truths in the sky. In both cases, the limited biological abilities of humans are assisted by hardware to extend the human reach.
There was no way for Galileo Galilei to imagine the discovery of the galaxy GN-z11 by HST. This galaxy existed during the cosmic dawn, 400 million years after the Big Bang, when the infant Universe was only 3% of its current age. Galileo did not know that stars emit light from so far away, nor that the Sun is late to the cosmic party since it formed in the last third of cosmic history. His concept of the world included the solar system and some bright stars near it. That was it.
Similarly, traditional mathematicians used the limited neural network at their disposal in their biological brain to explore mathematical truths in the domain accessible to their brain. As of now, SI helps us resolve open questions that were defined by these same human brains. But in the future, SI could reveal new mathematical truths that the human brain did not even imagine.
Whereas the revolution in our understanding of the cosmos was brought about by centuries of improving astronomical instrumentation, the SI revolution in mathematics takes place rapidly over a period of only months. It took the Vatican 350 years after the death of Galileo to admit that he was right. But it takes Lean at most hours to check math derivations by SI.
What are humans to do under these circumstances?
Mathematicians can learn from the historical precedence of astronomy in how to adapt to emerging technologies. The proper approach is to take advantage of technological assists and change the skills necessary for making breakthroughs. The expertise needed to take advantage of HST data is very different from that employed by Mayan astronomers.
The Physics Nobel Prize was awarded in recent decades to astronomers who did not necessarily have exceptional eyesight like the Mayan astronomers, but instead had the vision to employ the latest technologies to discover the faint radio glow from the Big Bang (here and here), the existence of black holes and neutron stars in the infrared (here), X-rays (here), gravitational waves (here) and neutrinos (here and in 2026 here).
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