Sixteen Ways to Reach a Valve: Algebraic Geometry Made Gentle

Deep End Era. Engineering with Sankalp · Oct 28, 2026 · 53m

Fictional robotics engineer Priya Raman's valve-handling arm suddenly returns sixteen valid ways to reach the same handwheel, and her uncle Desmond, a retired maths teacher, tells her the robot is secretly a system of polynomial equations. In episode one hundred and seventy one we build algebraic geometry from pictures, not symbols. We count intersections, follow Hilbert's dictionary between shapes and equations, and turn it into algorithms with Gröbner bases and homotopy continuation. Then we see Steiner's famous counting mistake, how elliptic curves proved Fermat's Last Theorem and now…