Blog
Blog
Technical articles on FEM analysis, cleanroom design, and the other fields Mathematical Physics Labo works in.
2026-09-30
AI Wrote a Proof. But What Did It Prove?
In September 2026, an AI system produced an answer to the Navier-Stokes Millennium Prize Problem, formalized and machine-checked. Here's what that event says about the practical question of how to verify AI-generated work.
2026-09-26
Can an Invention Made With AI Be Patented?
As generative AI becomes part of R&D, a new question arises: who counts as the inventor? We walk through where the U.S. and Japan currently stand, based on primary sources.
2026-09-25
Don't Let AI Judge the Calculations AI Produced
As AI takes on more analysis work, how do you verify whether its results are correct? Lessons from building structural and fluid analysis pipelines, on what mechanical verification actually means.
2026-09-22
In CFD, a Finer Mesh Doesn't Always Mean Higher Accuracy
An OpenFOAM case where refining the mesh 8x failed to reduce pressure-drop error shows why mesh shape, not just mesh density, determines CFD accuracy.
2026-09-09
Detecting Split Pit in Peaches Without Cutting Them Open
How an acoustic vibration method detects split pit in peaches without cutting them open, based on research that won the Japanese Society for Horticultural Science's annual best paper award.
2026-08-07
How Does a Mathematical Physics Consultant Differ from a CAE Engineer?
What separates a CAE engineer running FEM simulations from a mathematical physics consultant. Using the FEM value chain as a guide, this piece sets out Mathematical Physics Labo's position: working upstream, on formulating the problem, and in non-standard territory.
2026-07-27
Does FEM Consulting Lose Its Value in the Age of AI?
Generative AI has lowered the cost of running FEM analysis, but building the model and judging whether the results are sound still require specialist experience. On the value of mathematical science consulting in the age of AI.
2026-07-18
What Is FEM Analysis? The Case for Outsourcing, and What Our Work Shows
An introduction to finite element method (FEM) analysis, the benefits of outsourcing it, and the range of applications demonstrated by Mathematical Physics Labo's work.
2026-07-17
Why Cleanroom Design Tends Toward Overspecification: Optimizing Air Change Rates and Purifier Counts with Mathematical Models
The basics of cleanliness classes in cleanroom design, why designs tend to be overspecified, and how mathematical optimization cut construction cost in practice.