Decoding with the Rongdu Principle: Mathematicians and Basic Sciences Need Not Panic—AI Cannot Independently Solve the Core Problems of This Field; Humans Remain the Solvers

OpenAI's 165-page Navier-Stokes proof triggered a wave of panic: Is AI about to replace mathematicians? Will basic science be taken over by machines? The Rongdu Principle offers a calm and clear judgment: AI is a powerful logical engine, but the solution of core problems in this field still depends on humans. AI can accelerate 'well-defined subproblems,' but it cannot independently solve basic-science problems that require 'redefining the problem itself.'

I. AI's Real Capability Boundary: Subproblems vs. Meta-Problems

AI excels at: under given boundaries, given goals, and given axiomatic systems, conducting high-speed logical search, combinatorial enumeration, and formal verification. It can complete years of human derivation work in 88 hours.

But the core problems of basic science are often not 'solving within a given framework,' but rather:

• Redefining the problem: The Millennium Problem asks about 'no external force,' while AI went off to solve 'with external force.'
  
• Judging physical meaning: Is a mathematically self-consistent singularity physically permissible?
  
• Completing the cognitive transition: How does a 165-page symbol string transition into 'the essence of the Navier-Stokes equations'?
  
• Bearing paradigm responsibility: When a proof exceeds the limit of human comprehensibility, who decides whether it is accepted?
  

These are precisely the tasks that the 16 Principles of the Rongdu Principle reveal that AI cannot independently complete.

II. Item-by-Item Proof of the 16 Principles: Why AI Cannot Independently Solve the Core Problems of This Field

P0 (Meta-Self-Reference Principle): AI can modify its own parameters, but it cannot judge whether the 'objective function of modification' itself is legitimate. Who decides what AI should optimize? The answer is humans. The meta-rules of basic science are still set by humans.

P1 (Fluctuation Analysis Principle): AI can identify anomalous fluctuations, but it cannot judge whether a fluctuation is a 'physically valid signal' or 'numerical noise.' OpenAI treated the singularity as a signal, while physicists know it was an illusion manufactured by artificial external force.

P2 (Conservation Principle): AI can check whether an equation satisfies energy conservation, but it cannot judge whether 'finite total kinetic energy and infinite velocity' violates the physical conservation chain. The final right to judge physical reasonableness lies in human hands.

P3 (Fractal Growth Principle): The proof generated by AI has a fractal nested structure, which is efficient for machines to process but difficult for humans to understand. Reorganizing a fractal proof into human-comprehensible modules requires human cognitive participation.

P4 (Topological Constraint Principle): AI cannot judge whether 'adding an external force' changes the topological constraint of the original problem. The legitimacy of boundary conditions is not a logical issue, but an issue of consensus in the mathematical community.

P5 (Fission Principle): AI can execute a bifurcation between mathematical logical space and physical reality space, but it cannot choose which branch represents truth. Mathematics continues to explore logical possibilities; physics continues to guard the boundary of reality—this division of labor is maintained by humans.

P6 (Feedback Principle): The objective of AI's negative feedback optimization is set by humans. If the objective function is 'passing Lean verification,' AI will efficiently converge on 'logical compliance,' not 'solving the original problem.'

P7 (Structural Reuse Principle): AI is good at reusing existing proof frameworks (such as the Euler equation singularity construction), but it cannot create entirely new mathematical paradigms. Breakthroughs in basic science often require breaking old frameworks, not reusing them.

P8 (Homeostasis Principle): AI can optimize system stability, but it cannot decide whether a 'new homeostasis is acceptable.' Will the mathematics community accept a proof that is 'incomprehensible but machine-verified'? This is a human value judgment.

P9 (Boundary Reorganization Principle): AI can reorganize boundary conditions, but it cannot judge whether the reorganization is legitimate. Is reorganizing 'no external force' into 'with external force' innovation or substitution? Human mathematicians decide.

P10 (Dimensional Ascension Principle): AI can search in high-dimensional space, but it cannot judge the meaning of 'dimensional ascension.' The cognitive transition from 'mathematical proof' to 'AI capability evaluation' is completed by humans.

P11 (Solitary Wave Principle): A Lean formal proof is like a solitary wave, transmitting logic over long distances without distortion. But it transmits only 'logical correctness,' not 'intuitive meaning.' The attenuation of mathematical intuition can only be compensated for by humans.

P12 (Evolutionary Path Principle): AI's proof path depends on its search strategy. It cannot step outside a given path to ask, 'Have we asked the wrong question?' Reselecting the evolutionary path is a human privilege.

P13 (Boundary Coupling Principle): AI cannot complete the boundary coupling between mathematical logical space and physical reality space. Whether a mathematical conclusion penetrates into physical reality requires experiments and physical intuition to test.

P14 (Observer Intervention Principle): AI's output will change the evolutionary direction of the mathematics community, but AI is not the ultimate observer. Who judges whether this proof deserves a place in history? Human mathematicians do.

P15 (Cognitive-Material Transition Principle): AI generates symbol strings; humans assign meaning. The cognitive transition from '165 pages of derivation' to 'the Navier-Stokes equations possess a singularity' can only occur in the human brain.

P16 (Rongdu Annihilation and Transfer): AI's proof is ultimately decided by humans: whether it is annihilated into a textbook footnote or transferred into a new research direction. The right to attribute value always lies in human hands.

III. The Essence of Basic-Science Problems: Not Calculation, but Judgment

The core problems of basic science are usually not 'cannot be calculated,' but rather:

• Not knowing whether the question is asked correctly (P4, P9)
  
• Not knowing whether the answer has physical meaning (P2, P13)
  
• Not knowing whether the proof can be understood (P3, P11, P15)
  
• Not knowing whether a new paradigm should be accepted (P8, P14, P16)
  

These tasks cannot be independently completed by AI. AI can become the strongest 'derivation accelerator,' but it cannot become the 'legislator of science.'

IV. The New Role of Mathematicians and Basic Scientists: From Bookkeepers to Conductors

In the AI era, mathematicians and basic scientists need not panic, because their role is not to be replaced, but to be upgraded:

• Problem definers: Decide what problem AI should solve, rather than being led by AI's solutions.
  
• Boundary guardians: Judge which mathematical conclusions can enter physical reality.
  
• Meaning assigners: Transition AI's symbol strings into human-comprehensible scientific knowledge.
  
• Paradigm legislators: Decide whether new proofs and new theories are accepted by the academic community.
  

AI is the oar; humans are the compass. No matter how fast the oar is, it cannot replace the compass in deciding the course.

V. Conclusion: No Need to Panic—Upgrade Instead

OpenAI's Navier-Stokes proof is not a signal that AI will replace mathematicians, but a signal that AI has exposed its own boundaries. It proves that: AI can surpass humans on well-defined subproblems, but on the core problems of basic science—which require redefining the problem, judging physical meaning, and completing cognitive transitions—it still depends on humans.

Mathematicians and basic sciences need not panic. What they truly need to do is learn to steer AI, this fast horse, while holding tightly to the reins—the right to define problems, the right to judge boundaries, the right to assign meaning, and the right to legislate paradigms.

Basic science depends on humans, not because humans calculate faster, but because humans know what should be calculated, and what it means once calculated.

This article is based on the framework of the '16 Principles of the Rongdu Principle' of the Zhuanzhi Think Tank, systematically arguing that AI cannot independently solve the core problems of basic science, and that mathematicians and basic scientists are irreplaceable. For related Rongdu Principle decoding articles, see the official website of the Zhuanzhi Think Tank.