LIANG.WORLD

Professor Cheng Jingde's "Professor's Office" thought experiment is an elegant refinement of Searle's Chinese Room: can an external questioner, through only a finite number of question-answer exchanges, distinguish whether the person behind the door is a real professor or an LLM expert system possessing all of the professor's knowledge? This essay analyzes the questioner's knowledge paradox, the reversal of the Turing Test, the testability of LLM capability boundaries, the source of cognitive normativity, and the phenomenological dimension of the Other Minds problem, ultimately proposing six minimal necessary conditions for indistinguishability.

The Riemann Hypothesis over function fields was proved by Weil in 1948. This article retraces three proofs — Hasse (elliptic curves, 1933), Weil (Jacobians and surface intersection, 1948), and Grothendieck–Deligne (étale cohomology, 1974) — showing they share a single logical skeleton: the Frobenius operator turns zeros into eigenvalues, duality pairs them, and a positivity structure pins them to the critical circle. It then asks: why can't this machinery be transferred to the integers? The answer lies in three structural absences — no global Frobenius, no finite-dimensional cohomology, no base field.

The most comprehensive and systematic review of Hilbert's Eighth Problem—the Riemann Hypothesis—in the Chinese-speaking world. From Riemann's 1859 original paper through analytic continuation, explicit formulas, the prime number theorem, zero counting, critical line theorems, zero density estimates, L-function theory, Landau-Siegel zeros, to the cutting-edge Selberg positive proportion theorem and open conjectures. A faithful, expressive, and elegant account of the deepest dialogue between prime distribution and complex analysis.

Rootlessness is the chronic disease of this generation. It drains not your wallet but your enthusiasm for life. This essay offers a practical four-lesson process—knowing a city through your senses, caring about its future, showing up in public life, and allying with fellow travelers—to quickly put down roots in any city and replace rootlessness with belonging, inch by inch.

GPT-5.5 Pro independently discovered a two-dimensional counterexample, toppling the Fisher Information Log-Convexity Conjecture and its chain of implications — GCMC, McKean's Conjecture, Toscani's Entropy Power Conjecture. The "hexagonal perturbation" excited by a resonant triad on the triangular torus reveals the fragility of human intuition in high-dimensional nonlinear worlds — and the civilizational significance of silicon intelligence as the "midwife of thought."

Beginning at the Café des Phares beside Paris's Place de la Bastille in 1992, this guide weaves together Marinoff's PEACE process, Brenifier's Socratic questioning, Phillips's democratic facilitation, and Harteloh's philosophical walks, offering an actionable philosophical dialogue facilitation guide. The mission of the thought midwife: to return philosophy to everyone.