2025-11-07 –, Talk Track 2
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.
This talk explores the line between solvable and unsolvable equations by deliberately “cheating” with Python and SymPy. Instead of diving into advanced theory, we’ll probe different families of equations to see when closed forms appear and when numerical methods are the only option.
The topic is not only playful but also useful. Data scientists often use equations when building models, and knowing when to expect a closed form — and when to stop searching and rely on numerical methods — can save time and guide analysis.
We’ll also connect to history: Kepler struggled with orbital equations that resisted algebraic solutions, and Renaissance mathematicians staged public duels over cubic and quartic formulas. These stories echo the puzzles we can now probe directly with code.
Outline:
- Motivation: why some equations are solvable and others are not
- Historical context: Kepler, polynomial duels, and beyond
- Experiments with SymPy:
- Polynomials (quadratic through quintic)
- Exponentials and logarithms (Lambert W)
- Trigonometric equations (commensurate vs. non-commensurate)
- Mixed equations with x, exp(x), log(x), and trig
- Patterns and surprises discovered through experimentation
- Practical takeaways: when to expect closed forms, when to switch to numerical methods.
Knowledge needed: Basic Python familiarity. No advanced math background required — the examples will be self-contained and accessible.
No previous knowledge expected
Carl Kadie leads the FaST-LMM open-source Python project for genomics. He also contributes to other Python and Rust projects, including a visualizer for the Turning Machine bbchallenge.org website. Previously, Carl was a Principal Applied Scientist at Microsoft and Microsoft Research, where he worked in machine learning, statistics, and genomics, with publications in Science and Nature.
(On the side, he writes fun articles about Python, Rust, and scientific programming on Medium.)