Video: PyData Seattle Talk on Solvable and Unsolvable Equations with SymPy

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Carl K

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Nov 18, 2025, 10:32:18 AM (3 days ago) Nov 18

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Hi all,

I wanted to share a new PyData Seattle talk that may interest SymPy users. The talk explores a broad question: Which equations have closed-form solutions, and which never will?

To investigate this, I cheated. Instead of using advanced algebra, Galois theory, or transcendental number theory, I used Python and SymPy to probe families of equations:

polynomials (including degree ≥5),
equations mixing x with exp/log (Lambert W appears),
trigonometric equations with commensurate and non-commensurate frequencies,
and mixed combinations of trig, exp, and log.

The talk shows when SymPy succeeds symbolically, when it falls back to numerical methods, and when equations seem fundamentally unsolvable in closed form.

New Video: https://www.youtube.com/watch?v=02Bchtfb0AI
Free article: https://medium.com/data-science/explore-solvable-and-unsolvable-equations-with-python-661ac11f4f20

Thanks to everyone who contributes to SymPy. It’s an excellent tool for exploring these questions.