π as a Definable Irrational Number

π as a Definable Irrational Number is the premise at the heart of Rong Jinzhen’s graduation thesis: an attempt to use a mathematical constant to address a major problem in artificial intelligence. The thesis turns on a productive but unresolved tension. Its argument reaches from the properties attributed to π toward the limits of reproducing human intelligence, yet its larger claims depend on accepting an assumption about π that the thesis does not establish.

The thesis and its setting

Rong Jinzhen’s thesis took up a subject far beyond the material he had studied in class, one the account describes as more appropriate to a master’s thesis. Its title was “The Constant π as a Definable yet Irrational Number.” The work grew in part from books Rong Jinzhen had been reading in the attic, and it brought an unusually ambitious mathematical question into his university studies.

The choice was also made in a politically sensitive climate. The validity of Georg Weinacht’s theories was rejected in a number of communist countries led by the Soviet Union; when his work was discussed, it was often criticized. At a time when others hoped Rong Jinzhen would abandon the subject, Young Lillie instead became his supervisor and encouraged him to continue. Young Lillie’s support gave the thesis room to develop, but it also became part of the later uncertainty about who had produced it.

From a mathematical constant to artificial intelligence

The thesis takes π as its starting point and develops Georg Weinacht’s binary theory into a proposed solution to a major problem in artificial intelligence. Its striking further step is to treat human intelligence as a mathematical constant and an irrational number that never comes to an end. In this conception, intelligence is not simply a finished quantity that can be exhaustively captured and reproduced.

The argument gives a central role to confusion. Human intelligence, the thesis proposes, includes an element of confusion that is indefinable: it cannot be known completely and therefore cannot be replicated. On that basis, Rong Jinzhen argues that, under present conditions, artificial systems can approach human intelligence but cannot reproduce it entirely. The thesis’s significance lies less in claiming that machines can accomplish a close approximation than in marking a limit that the theory regards as intrinsic to human thought.

The account presents the work’s achievement as a daring derivation rather than a wholly new conclusion. Many mathematicians, including contemporary ones, share the position that human intelligence cannot be fully reproduced. What is distinctive is Rong Jinzhen’s attempt to derive that position from a hypothesis about the binary nature of π and to develop its consequences through pure mathematics. The thesis tries to make the claim demonstrable rather than leave it as an intuition.

Proof, assumption, and the unstable foundation

The thesis’s strength and weakness arise from the same starting point. Rong Jinzhen builds a chain of reasoning from π treated as a constant. If that premise is accepted, the work’s progression from a mathematical constant to a theory of human intelligence is presented as a powerful transformation: a difficult problem in artificial intelligence becomes approachable through a formal mathematical argument. The account likens the effect to catching invisible wind in a human hand.

But the proofs cannot establish more than their starting assumption permits. The thesis does not first prove that π is genuinely a constant, and its proofs therefore rest on a foundation that remains in question within the book’s discussion. The account notes that the issue had been raised centuries earlier and had not, in its telling, been conclusively proved. Although most mathematicians are described as believing π to be constant, the absence of proof leaves room for disagreement. The comparison to Newton’s account of universal gravity underscores the distinction between a widely accepted proposition and one that has been demonstrated to everyone’s satisfaction.

That distinction makes the thesis conditional. If a reader rejects the premise that π is a constant, the argument built upon it collapses and the thesis is useless on its own terms. If the premise is accepted, the work’s audacity becomes visible: it bends a mathematical starting point into an account of the irreducible complexity of human intelligence. The thesis can thus appear both ingenious and precarious, its reach extending beyond what its unproved foundation can securely bear.

Composition, reception, and attribution

Young Lillie’s response to the first draft was enthusiastic. He admired the incisive, logical thinking but found some of the mathematical proofs unnecessarily complicated. His revisions aimed to simplify their presentation and remove needless elements; developing the basic proofs sometimes required sophisticated, direct methods that demonstrated understanding beyond mathematics alone. The first draft ran to 20,000 characters. After two rounds of revision, the final version was just over 10,000.

The finished thesis was published in Popular Mathematics and made a substantial impression in Chinese mathematical circles. Its revised form also created a problem of authorship in the eyes of some readers: the quality seemed too polished for an undergraduate thesis, and many suspected that Rong Jinzhen could not have done it all himself. The very editing that clarified the proofs therefore helped obscure the achievement it was meant to present.

Master Rong later insisted that Rong Jinzhen had written the thesis independently. According to her account of what Young Lillie told her, he recommended a couple of reference books and wrote the introduction, but contributed none of the mathematical contents. In that introduction, Young Lillie cast Georg Weinacht’s theories as a demon within scientific research and presented the thesis as a challenge to them. His framing made the project more than a technical exercise: it was also an attempt to contest a theory that had been treated as politically and intellectually dangerous.

Significance and consequences

The thesis’s value remains suspended between its ambition and its unproved premise. If π is established as the kind of constant the argument requires, the thesis’s proposed route from pure mathematics to a limitation on artificial intelligence gains academic weight. Until then, the book describes its strict academic success as uncertain: the work demonstrates Rong Jinzhen’s intelligence and daring more securely than it proves its central theory.

Its personal consequences are similarly divided. The thesis did not change Rong Jinzhen’s life, but it left his authorship and genius open to doubt because his connection with Young Lillie made the polished result seem collaborative. For Young Lillie, by contrast, the thesis changed the final years of his life. The concept therefore stands in the narrative as both an ambitious intellectual construction and an incomplete proof: a work whose most compelling claim reaches beyond the ground it has yet secured.