You can know everything happening inside a shape without ever looking inside it - just walk around the edge. It sounds impossible, and it's the trick that makes physics AI actually run.
take any swirling 2D field -> measuring all the rotation inside means summing infinitely many points -> Green's theorem says that entire interior equals a single loop around the boundary -> the inside cancels itself out, only the edge survives -> an area problem becomes an edge problem.
That loop is why fluid simulators, graphics engines and every physics-AI model fake reality fast - instead of computing every point in a region, they only touch its boundary, and a 200-year-old theorem guarantees it's the exact same answer.
Watch and bookmark it, then see the edge-trick quietly powering every physics simulation in AI
You can take half a derivative. Not the 1st, not the 2nd - the 0.5th. It sounds made up, mathematicians sat on it for 300 years, and it's quietly becoming the math behind how AI remembers.
a normal derivative is "local" - it only knows the single point you give it -> but the real world has memory: the present depends on the entire past -> a fractional derivative kills that locality and keeps the whole history -> the 0.5th derivative literally carries a function's entire past -> that's fractional calculus.
That loop is why fractional calculus is creeping into modern AI - the long-range memory transformers burn billions of parameters to fake is native to a 300-year-old operator almost no engineer has touched.
Watch and bookmark it, then see the half-derivative quietly teaching machines to remember
Every probability an AI computes - every loss, every expected reward - is secretly an integral your calculus class was too weak to solve. A French mathematician fixed it by turning the integral sideways.
slice the area into vertical strips (Riemann) -> hit a function it literally can't integrate -> flip it, slice horizontally by output value instead -> the "impossible" ones suddenly work -> that's the Lebesgue integral.
That loop is why all of modern probability - every expected value inside ChatGPT, AlphaGo and every trained model - runs on a 100-year-old integral almost no engineer has actually seen.
Watch and bookmark it, then see the integral quietly running every AI's math
Every AI trying to predict the real world eventually crashes into the same 200-year-old equation nobody has ever solved. There's a $1,000,000 prize sitting on it right now.
fluid flows → mass can't vanish → F=ma on a single drop → add pressure + friction → the Navier-Stokes equations.
That loop is why DeepMind's weather AI, every Tesla sim and every rocket engine on Earth run on math we bet billions on but still can't prove won't break - it's the reason no one can tell you the weather past 7 days.
Watch and bookmark it, then understand the one equation modern AI still can't beat
İçişleri bakanına göre çok uzun süredir önlem alınmasaymış çok büyük bir kaos ile karşı karşıya kalınabilirmiş. İçişleri bakanına göre 40.000’den fazla insanımızın ölmesi çokta büyük bir kaos değilmiş. Vay be…