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Category: mathematics – Page 4

Scientist Connected Light And Matter a Century Before Quantum Physics

The Irish mathematician and physicist William Rowan Hamilton, who was born 220 years ago last month, is famous for carving some mathematical graffiti into Dublin’s Broome Bridge in 1843.

But in his lifetime, Hamilton’s reputation rested on work done in the 1820s and early 1830s, when he was still in his twenties. He developed new mathematical tools for studying light rays (or “geometric optics”) and the motion of objects (“mechanics”).

Intriguingly, Hamilton developed his mechanics using an analogy between the path of a light ray and that of a material particle.

CWM: An Open-Weights LLM for Research on Code

We release Code World Model (CWM), a 32-billion-parameter open-weights LLM, to advance research on code generation with world models. To improve code understanding beyond what can be learned from training on static code alone, we mid-train CWM on a large amount of observation-action trajectories from Python interpreter and agentic Docker environments, and perform extensive multi-task reasoning RL in verifiable coding, math, and multi-turn software engineering environments. With CWM, we provide a strong testbed for researchers to explore the opportunities world modeling affords for improving code generation with reasoning and planning in computational environments. We present first steps of how world models can benefit agentic coding, enable step-by-step simulation of Python code execution, and show early results of how reasoning can benefit from the latter.

Scientist Connected Light And Matter Century Before Quantum Physics

The Irish mathematician and physicist William Rowan Hamilton, who was born 220 years ago last month, is famous for carving some mathematical graffiti into Dublin’s Broome Bridge in 1843.

But in his lifetime, Hamilton’s reputation rested on work done in the 1820s and early 1830s, when he was still in his twenties. He developed new mathematical tools for studying light rays (or “geometric optics”) and the motion of objects (“mechanics”).

Intriguingly, Hamilton developed his mechanics using an analogy between the path of a light ray and that of a material particle.

The Hunt for Dark Matter Has a New, Surprising Target

Dark Matter remains one of the biggest mysteries in fundamental physics. Many theoretical proposals (axions, WIMPs) and 40 years of extensive experimental search have not explained what Dark Matter is. Several years ago, a theory that seeks to unify particle physics and gravity introduced a radically different possibility: superheavy, electrically charged gravitinos as Dark Matter candidates.

A recent paper in Physical Review Research by scientists from the University of Warsaw and the Max Planck Institute for Gravitational Physics shows that new underground detectors, in particular the JUNO detector that will soon begin taking data, are well-suited to detect charged Dark Matter gravitinos even though they were designed for neutrino physics. Simulations that bridge elementary particle physics with advanced quantum chemistry indicate that a gravitino would leave a signal in the detector that is unique and unambiguous.

In 1981, Nobel Prize laureate Murray Gell-Mann, who introduced quarks as fundamental constituents of matter, observed that the particles of the Standard Model—quarks and leptons—appear within a purely mathematical theory formulated two years earlier: N=8 supergravity, noted for its maximal symmetry. N=8 supergravity includes, in addition to the Standard Model matter particles of spin 1/2, a gravitational sector with the graviton (of spin 2) and 8 gravitinos of spin 3/2. If the Standard Model is indeed connected to N=8 supergravity, this relationship could point toward a solution to one of the hardest problems in theoretical physics — unifying gravity with particle physics. In its spin ½ sector, N=8 supergravity contains exactly 6 quarks (u, d, c, s, t, b) and 6 leptons (electron, muon, taon and neutrinos), and it forbids any additional matter particles.

A scalable and accurate tool to characterize entanglement in quantum processors

Quantum computers, computing systems that process information leveraging quantum mechanical effects, could soon outperform classical computers in various optimization and computational tasks.

To enable their reliable operation in real-world settings, however, engineers and physicists should be able to precisely control and understand the quantum states underpinning the functioning of .

The research team led by Dapeng Yu at Shenzhen International Quantum Academy, Tongji University and other institutes in China recently introduced a new mathematical tool that could be used to characterize quantum states in quantum processors with greater accuracy.

Physicist proves unsolvability beyond one dimension for quantum Ising models

By extending a proof of a physically important behavior in one-dimensional quantum spin systems to higher dimensions, a RIKEN physicist has shown in a new study that the model lacks exact solutions. The research is published in the journal Physical Review B.

Theoretical physicists develop mathematical models to describe material systems, which they can then use to make predictions about how materials will behave.

One of the most important models is the Ising model, which was first developed about a century ago to model such as iron and nickel.

Light-Powered AI Chips: The Photonic Revolution That’s About to Change Everything

Light-Powered AI Chips: The Photonic Revolution That’s About to Change Everything ## The future of artificial intelligence (AI) may be revolutionized by photonic AI chips that use light instead of electricity to process information, enabling faster, more efficient, and heat-free computing.

## Questions to inspire discussion.

Photonic AI Technology.

🔬 Q: What makes photonic AI chips more efficient than current AI chips? A: Photonic AI chips are 100x more energy efficient and produce virtually zero heat compared to electronic chips, as they use light instead of electrons for computation.

🌈 Q: How do photonic chips encode information differently? A: Photonic chips can encode information simultaneously in wavelength, amplitude, and phase by bouncing light off mirrors and optical devices, replacing traditional electronic processors.

Industry Developments.

Continue reading “Light-Powered AI Chips: The Photonic Revolution That’s About to Change Everything” | >

Google DeepMind discovers new solutions to century-old problems in fluid dynamics

For centuries, mathematicians have developed complex equations to describe the fundamental physics involved in fluid dynamics. These laws govern everything from the swirling vortex of a hurricane to airflow lifting an airplane’s wing.

Experts can carefully craft scenarios that make theory go against practice, leading to situations which could never physically happen. These situations, such as when quantities like velocity or pressure become infinite, are called ‘singularities’ or ‘blow ups’. They help mathematicians identify fundamental limitations in the equations of fluid dynamics, and help improve our understanding of how the physical world functions.

In a new paper, we introduce an entirely new family of mathematical blow ups to some of the most complex equations that describe fluid motion. We’re publishing this work in collaboration with mathematicians and geophysicists from institutions including Brown University, New York University and Stanford University.

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