The Quanta Podcast Mathematicians Want To Make Fluid Equations Glitch Out
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Feb 10, 2026 Charlie Wood, a Quanta Magazine staff writer who covers physics and math, discusses the math behind rivers, whirlpools and breezes. He explains how Navier‑Stokes equations can allow mathematical “glitches” called singularities. Conversation covers what blowups mean, how simulations and AI help find unstable candidates, and why viscosity and stability matter.
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Math Solutions Can Be Nonphysical
- The Navier-Stokes equations are differential equations that describe fluids and their many possible behaviors.
- Some mathematical solutions can be undefined or nonphysical, creating singularities like blowups that lack real-world meaning.
Treat Simulation Crashes As Clues
- Use simulations as diagnostic tools but verify suspected blowups against the continuous equations.
- Treat computer crashes or runaway velocities as cues to examine the underlying math, not definitive proof of singularities.
Stable Versus Unstable Singularities
- Stable singularities persist under small perturbations and can be detected in pixelated simulations.
- Unstable singularities are extremely sensitive to tiny changes and disappear under slight perturbations, making them invisible to standard simulations.
