DeepMind and collaborators present a new way for artificial intelligence to act like a mathematical magnifying glass: they found families of unstable singularities in equations that have been challenging researchers for more than a century. What does this mean for physics, mathematics and engineering? Let’s take it step by step with clear examples.

What did they announce exactly

On September 18, 2025 DeepMind published an article explaining that, together with mathematicians and geophysicists from institutions like Brown, NYU and Stanford, they have identified new families of “blow ups” or unstable singularities in several fluid dynamics equations. (deepmind.google)

The technical work is available on arXiv under the title "Discovery of Unstable Singularities" and was uploaded on September 17, 2025. In that document the authors describe self-similar solutions for equations like incompressible porous media and variants of Euler, and show an empirical relationship between the collapse rate and the order of instability. (ar5iv.org)

Why this matters (yes, it matters a lot)

Singularities are points where physically relevant quantities, like velocity or pressure, can tend toward infinity. Some of these phenomena are central to deep questions in pure mathematics, including those related to the Millennium problems — think of the Navier–Stokes case. That an AI helps discover new families of singularities opens the door to different ways of exploring these problems and to building computer-assisted proofs. (deepmind.google)

Think of it like finding secret paths on a mountain map that looked flat: knowing those routes changes how you model erosion, rainfall, or the behavior of a reactor where fluids matter.

How they did it: a mix of mathematical ideas and AI

This wasn't just about training networks on lots of data. The team used PINNs (Physics Informed Neural Networks), networks that learn to respect the physical equations by continuously checking their outputs against the PDEs governing the system. They also introduced improvements in architecture and training, including second-order optimizers and a high-precision framework that reaches near machine precision. That made it possible to detect solutions extremely sensitive to perturbations — in other words, unstable singularities. (deepmind.google)

"By integrating mathematical knowledge and pushing precision to the extreme we transformed PINNs into a discovery tool." (Yongji Wang, lead author). (deepmind.google)

Key results in plain terms

• They found new families of unstable singularities in at least three different fluid dynamics equations. (deepmind.google)
• They observed a reproducible pattern: the collapse rate (the lambda in the paper) seems to follow a law as the order of instability increases. (deepmind.google)
• They reached precision levels that can support future attempts at computer-assisted mathematical proofs. (ar5iv.org)

What could change in practice?

It’s not that tomorrow the weather forecast will be completely different, but it does change tools and methods. Some plausible applications:

• New techniques to validate numerical models in engineering and geoscience simulations. (deepmind.google)
• Frameworks to develop computer-assisted mathematical proofs with very high precision requirements. (ar5iv.org)
• Inspiration to improve simulation algorithms in areas where small instabilities cause large effects, like aeroelasticity or certain ocean phenomena.

Limits and open questions

The keyword here is unstable. Unstable singularities require initial conditions tuned with extreme precision, so not all of them are relevant for physically observable phenomena in nature. Detecting them helps map the mathematical landscape of the equations, but distinguishing what’s mathematically possible from what’s physically likely remains additional work. (ar5iv.org)

There are also questions about reproducibility at larger scale, dependence on hardware for precision, and how far these techniques can be applied to more complex systems like Navier–Stokes with boundaries.

Readings and resources (to go deeper)

• DeepMind blog post with an accessible explanation and visualizations. (deepmind.google)
• Paper on arXiv: "Discovery of Unstable Singularities" (PDF and HTML available). Read on arXiv. (ar5iv.org)

For you, who want to understand or apply this

If you want to experiment: start by reading about PINNs and hands-on PDE exercises with neural networks. If you’re a researcher, check the repository and numerical methods in the paper to see how to adapt them to your problem. If you’re an entrepreneur or engineer, ask which design decisions could benefit from models that identify subtle instabilities before they become costly failures.

The news is an invitation. AI no longer just automates repetitive tasks; it’s becoming a tool for mathematical exploration that can point to territories no one had looked at before. Isn’t that exciting?