Generative AI can produce the "miraculous" insights needed for formal proofs, like finding an inductive invariant, which traditionally required a PhD. It achieves this by training on vast libraries of existing mathematical proofs and generalizing their underlying patterns, effectively automating the creative leap needed for verification.

The pattern of water hitting a sink basin—a smooth central circle, an outer ridge, and choppy water beyond—is mathematically identical to the inside of a black hole, its event horizon, and the surrounding open space. This provides a tangible, everyday visualization for a complex astrophysical concept.

Even Donald Hoffman, proponent of the consciousness-first model, admits his emotions and intuition resist his theory. He relies solely on the logical force of mathematics to advance, demonstrating that groundbreaking ideas often feel profoundly wrong before they can be proven.

Long before Einstein's relativity, scholars like Pierre-Simon Laplace and John Michell theorized about "dark stars." They reasoned that if a star were massive enough, its escape velocity could exceed the speed of light, trapping light and rendering it invisible. This early concept was based entirely on Newton's laws of gravity, demonstrating remarkable scientific foresight.

The Standard Model of particle physics was known to be incomplete. Without the Higgs boson, calculations for certain particle interactions yielded nonsensical probabilities greater than one. This mathematical certainty of a flaw meant that exploring that energy range would inevitably reveal new physics, whether it was the Higgs or something else entirely.

Our current computation, based on Turing machines, is limited to "computable functions." However, mathematics shows this set is a smaller, countable infinity compared to the vast, larger infinity of non-computable functions. This implies our current simulations barely scratch the surface of what is mathematically possible.

The singularity at a black hole's center is not a place in space but an inevitable moment in time for anything that crosses the event horizon. This conceptual flip means that trying to escape the singularity is as futile as trying to avoid next Tuesday. The flow of spacetime itself pulls everything inward toward a future point of infinite density.

To move beyond current paradigms, one must simultaneously engage in rigorous mathematical thinking and the practice of letting go of all concepts through deep meditation (silence). This mirrors quantum computing, which requires precise setup followed by non-interference. Sloppy, middle-ground thinking yields no reward; only the two extremes push boundaries.

AI is developing spatial reasoning that approaches human levels. This will enable it to solve novel physics problems, leading to breakthroughs that create entirely new classes of technology, much like discoveries in the 1940s led to GPS and cell phones.