Why can we solve some equations with neat formulas, while others stubbornly resist every trick we know? Equations with squares bow to the quadratic formula. Those with cubes and fourth powers also have solutions. But then the magic stops. And when we, as data scientists, add exponentials, logarithms, or trigonometric terms into models, the resulting equations often cross into territory where no closed-form solutions exist.

This talk is both fun and useful. With Python and SymPy, we’ll “cheat” our way through centuries of mathematics, testing families of equations to see when closed forms appear and when numerical methods are our only option. Attendees will enjoy surprising examples, a bit of mathematical history, and practical insight into when exact solutions exist — and when to stop searching and switch to numerical methods.