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Caihao Cui

Caihao Cui

Knowledge Grounds Action; Learning Nurtures Virtue.

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A serene, lush forest with a single, brightly colored, rare bird gently landing on a branch of a flourishing tree, observed from a distance, symbolizing that the most precious things appear when nurtured indirectly rather than directly pursued.

By-products: Most Precious Things Cannot Be Directly Pursued

31 July 2026·3321 words·16 mins

A stylized depiction of the evolution of mathematical knowledge. Digital, glowing threads representing AI-generated proofs emerge rapidly from one side, while human hands or figures on the other carefully weave, validate, explain, and consolidate these raw outputs into a robust, structured theoretical framework, symbolizing the shift from proof generation to understanding and responsibility in the age of AI.

Mathematics in the Age of AI: Terence Tao's Vision for the Mathematical Community

31 July 2026·3088 words·15 mins

A metaphorical image depicting a human mind in a state of profound self-reflection, illustrated with intricate, layered thought patterns and abstract symbols. Some layers represent first-order desires and ingrained frameworks, while higher, more luminous layers are actively observing, questioning, and re-shaping them. A central, detached light or energy symbolizes a mind that 'abides nowhere,' achieving freedom by transcending its own internal structures. The overall mood is contemplative and empowering.

Second-Order Volition and Metarepresentation: Give Rise to a Mind That Abides Nowhere

31 July 2026·3503 words·17 mins

An intricate system of precision gears, where each gear's deliberate and limited movement ensures the powerful and reliable operation of the entire mechanism, symbolizing how self-restraint enables complex systems and builds trust through reliable, constrained actions.

Self-Restraint: Power Through Limitation

31 July 2026·3445 words·17 mins

A reflective illustration of a person standing at a crossroads, with different paths illuminated by contrasting social values and opportunities: skyscrapers suggesting ambition, and a quiet landscape suggesting work-life balance. A glow around the figure's head evokes clarity of mind amid the interplay of effort, choice, and circumstance.

Clarity of Mind: As Times Change, What Do Effort and Choice Mean?

30 July 2026·4320 words·21 mins