Uncover the latest and most impactful research in Partial Differential Equations on Manifolds. Explore pioneering discoveries, insightful ideas and new methods from leading researchers in the field.

Physics-informed neural networks (PINNs) often struggle to solve stiff partial differential equations (PDEs) with moving boundaries, such as convection-dominated droplet drying with shrinking domains ...

The Navier-Stokes problem concerns equations of fluid motion, illustrated here as dye moving in liquid. Kterletska via Wikimedia Commons under CC BY 4.0 The Navier-Stokes problem, a famous theoretical ...

The mathematics community is still in shock. On September 8, 2026, OpenAI announced that an artificial intelligence model may have solved one of the most significant problems in the field, the ...

Molds are usually not a problem indoors, unless mold spores land on a wet or damp spot and begin growing. Molds have the potential to cause health problems. Molds produce allergens (substances that ...

Today may go down as the biggest day in math in at least two decades, if not far longer. In a development that crystallizes an existential shift in humankind’s oldest intellectual discipline, ...

You're currently following this author! Click to unsubscribe from email alerts. Math is hard. And, apparently, expensive. On Tuesday, OpenAI said its agents had solved the Navier-Stokes equations, a ...

All the Latest Game Footage and Images from University of Problems Student life is perhaps the most vivid, colorful, and memorable period of life for many of us. You start your adult life, feel ...

OpenAI claims one of its AI models has found a solution to the Navier-Stokes problem, one of the toughest and most enduring puzzles in mathematics, sitting on the list of Millennium Prize Problems, ...

Sam Altman has in recent years become one of the most well known tech CEOs in the world. OpenAI says it has found a solution to a decades-old advanced maths problem in a matter of hours using a new ...

OpenAI says it has found a solution to a decades-old advanced maths problem in a matter of hours using a new artificial intelligence (AI) model and thousands of AI bots. The ChatGPT-maker said on ...

OpenAI on Tuesday said its artificial intelligence technology has cracked one of the Millennium Problems –– seven famously difficult and unsolved questions in mathematics that have stumped even the ...