Terence Tao, a living legend and Fields Medalist, warns that science is entering a zone of turbulence comparable to the great "foundational crisis" of the early 20th century. Back then, Russell's paradox and Gödel's incompleteness theorems shattered the cozy assumptions of what defined a number or a set. Today, history is repeating itself, but artificial intelligence is the sledgehammer. As Tao noted, the question is no longer whether machines can calculate, but how quickly the academic community can adapt its values to tools capable of research-level problem solving.
A Paradigm Shift: From Intuition to Formal Code
Fundamental science is bracing for a great migration—moving away from human intuition toward rigid machine formalization. According to Tao, ignoring this shift is only viable if one assumes the technology will prove to be a long-term dud. However, current data, even when gathered under "wild" conditions, proves otherwise. AI isn't just automating routine tasks; it is redefining the very essence of proof and basic categories like number, infinity, and truth.
"The question is how we adapt our human values to these new capabilities," Tao emphasizes, hinting that mathematics is ceasing to be the exclusive domain of the human mind.
For the business world, this scientific drift serves as a deeply pragmatic signal. If even in the most rigorous of disciplines, the human "gut feeling" is no longer the yardstick of truth, then the management of autonomous systems will undergo a final shift: from trying to "understand how it thinks" to the mathematical verifiability of results. We are moving into a world where trust is built not on an affinity for an algorithm, but on a formal proof of its reliability.
Mathematics is losing its "naive" reliance on human understanding. Formalization is becoming the only way to verify complex AI systems. Intuitive management in business is giving way to rigid process verification. Foundations Crisis 2.0 requires a complete reassembly of decision-making logic.
In this new reality, the bedrock of logic is being rebuilt under machine supervision, and legacy verification methods simply cannot handle the weight of modern challenges. Those who continue to rely on "instinct" when managing complex systems risk finding themselves sidelined in a standardized world ruled by evidentiary efficiency rather than human guesswork.