Mathematicians at OpenAI showed that the Navier-Stokes equations, which describe how fluids flow, can sometimes “blow up.” But the massive result is not without controversy.
Category: information science – Page 2
AI extracts interpretable constitutive laws directly from solid-mechanics data
Researchers at the Eastern Institute of Technology (EIT), Ningbo, have developed a graph-based approach that directly extracts concise, accurate constitutive equations from solid-material experimental data. The study, published in Science Advances, describes a method for discovering constitutive models for alloy steels, lithium metal and filled rubbers. It outperforms mainstream empirical models in predictive accuracy while preserving explicit, physically interpretable mathematical formulations.
This breakthrough addresses a longstanding limitation in solid mechanics: the conventional reliance on predefined empirical formulas to characterize the complex mechanical responses of metallic and nonmetallic materials. “Constitutive models are foundational to solid mechanics. Traditionally, researchers derive mathematical forms based on physical intuition and subsequently calibrate model parameters using experimental data,” said Hao Xu, EIT postdoctoral researcher and lead author of the study.
“Although this paradigm has achieved great success in mechanics research, predetermined equation structures inherently restrict the model’s descriptive and predictive capability. Our framework shifts the research paradigm: it starts purely from experimental data and employs artificial intelligence to autonomously search for and identify optimal constitutive equations.”
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TianGong Ultra Beat Usain Bolt’s Record, But Braking Remains Unsolved
TianGong Ultra Beat Usain Bolt’s 100m Record — Then Admitted It Can’t Brake Safely.
China’s TianGong Ultra ran 100 meters in 8.64 seconds at the World Humanoid Robot Games (Usain Bolt’s record: 9.58s).
Impressive speed. Real sim-to-real transfer under competition pressure.
But the robot’s own lead engineer said braking remains unsolved. At 75 kg and speeds over 17 m/s, the robots used crash mats because safe stopping wasn’t ready yet.
This is a genuine technical achievement. It is not yet commercial readiness.
For anyone evaluating humanoids for industrial use: competition records are exciting, but the ability to stop safely at those speeds is the real question that matters.
Full analysis:
On the Navier–Stokes Millennium Prize Problem
We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean.
The Millennium Prize Problems (opens in a new window) represent some of the deepest questions at the frontier of mathematics. The question of whether smooth three-dimensional fluid motion can break down has remained unresolved for roughly 90 years.
Stable Singularity of the Euler Equations on R^3 without forcing
In the theory of partial differential equations (PDEs), an important problem is analyzing whether there is loss of regularity in finite time, even when there is smooth initial data. This is known as singularity formation, or blowups. A famous one is whether fluid dynamics represented by Navier-Stokes equations experiences such blowups, and is one of the unsolved Millennium prize problems.
A closely related problem is known as the Euler problem and it represents inviscid flow, i.e., it lacks the viscosity term present in the Navier-Stokes equation. Intuitively the lack of viscosity makes it easier for blowups to happen, but it is still an open problem if such blowups occur in free space (R^3).
Treatment strategies and innovation for recurrent highgrade glioma NeuroOncology
Recurrent high‑grade glioma (HGG)—including glioblastoma—remains lethal, with median survival of approximately 6–10 months after first progression, although patients with IDH mutant tumors often have better survival. Recent ASCO/SNO data and expanding trial data are reshaping available treatment strategies.
We review evidence for alkylators and anti‑angiogenic therapy; summarize targeted options for rare, actionable alterations; review immuno‑oncology combinations and cellular therapies; highlight DNA damage response (DDR)/radiosensitization strategies and discuss advances in blood–brain barrier modulation and locoregional delivery. We propose a patient‑centered algorithm that prioritizes trial enrollment, biomarker‑guided approaches, steroid stewardship, and quality of life.
Lomustine, temozolomide rechallenge, and bevacizumab remain commonly used but provide modest benefit. Targeted agents show meaningful activity only in select subsets (BRAF V600E, NTRK). DDR-directed agents such as ATM/ATR inhibitors show early promise. Immunotherapy advances center on rationale combinations, oncolytic viruses, and locoregionally delivered CAR-T/TCR platforms. Blood-Brain-Barrier (BBB) modulation strategies and adaptive trials are broadening access to innovative therapies. The 2025 landscape features meaningful, if incremental, options—alongside the first ever FDA‑approved therapy for H3K27M‑mutant diffuse midline glioma at relapse—and a pipeline of rational combinatorial approaches poised to refine outcomes for selected patients. This article concentrates on medical options and intentionally omits extended discussions of surgery and radiation beyond their integration with systemic therapies at recurrence.
Scientists Just Challenged a Century-Old Theory of How Crystals Form
3D atomic imaging of advanced materials provides new insights into transitions such as liquids freezing into solids.
For nearly a century, scientists have relied on classical nucleation theory to explain how phase transitions such as freezing and condensation get started. The theory describes how small, ordered regions called nuclei emerge within disordered matter, and a central equation behind that picture has been supported by thousands of experiments.
But when UCLA-led researchers examined crystal formation atom by atom in three dimensions, the nuclei did not look the way the classical model predicts.
Dual-purpose qubit design could speed operations while cutting quantum errors
Researchers from MIT have designed a new qubit architecture that enables qubits to interact with each other much more quickly while remaining very stable. This advance could someday help scientists build practical quantum computers that can run long, complex algorithms with high accuracy.
Qubits, which are the building blocks of a quantum computer, usually only store data and rely on other electronics to perform operations and communicate. But qubits are so fragile and error-prone that it is difficult for scientists to connect enough qubits before they lose their information and need to be reset.
The MIT team designed a dual-purpose qubit with two separate parts: one component that stores data and one component that interacts with other qubits and electronics. This design improves the reliability of the qubit and enables it to operate with a reduced error rate, so it can perform more computations in the same time span.
Quantum control algorithm looks to explain how birds migrate
The hidden world of quantum mechanics exists at scales many orders of magnitude smaller than living organisms, yet scientists have long theorized that quantum effects play an important role in biology. Birds’ ability to sense magnetic fields during migration is one of the best-known mysteries in this field, with leading theories suggesting that this sensing could be achieved by exploiting quantum entanglement.
By proving a mathematical principle about how best to control quantum systems, researchers at the Okinawa Institute of Science and Technology (OIST) have taken what could be the penultimate step toward finally putting this avian hypothesis to the test, while also unlocking new biological platforms for quantum computing. Their results are published in the journal Quantum.
Ugur Abdulla, head of the Analysis and Partial Differential Equations Unit at OIST, explains, “Many researchers have studied quantum effects and their role in biology, though it isn’t always easy to translate an idea or hypothesis into a laboratory experiment. We hope that by laying the mathematical foundation for controlling quantum phenomena, we can bring some of these ideas from quantum biology out of the theoretical realm and into the lab.”