Lifeboat Foundation

A mathematician at Yonsei University, in Korea, claims to have solved the moving sofa problem. Jineon Baek has posted a 100+-page proof of the problem on the arXiv preprint server.

Most people who have moved their place of residence have encountered the moving sofa problem—it comes up when attempting to carry a couch around a corner. What is the largest couch that can be carried around a given corner without getting stuck? This problem was posited mathematically by mathematician Leo Moser back in 1966, and until now, has remained unsolved.

Moser’s initial thoughts centered on the possibility of developing a proof showing how mathematics could be used to solve any such problem using a given shape of a plane as it was moved around a right-angled corner of an empty space (such as a hallway) that was one unit in width.

Cellular death is a fundamental concept in biological sciences. Despite its importance, its definition varies depending on the context in which it occurs and lacks a general mathematical definition.

Researchers from the University of Tokyo propose a new mathematical definition of death based on whether a potentially dead cell can return to a predefined “representative state of living,” which are the states of being that we can confidently call “alive.” The researchers’ work could be useful for biological researchers and future medical research.

While it’s not something we like to think about, death comes for us all eventually, whether you’re an animal, a plant, or even a cell. And even though we can all differentiate between what is alive and dead, it might be surprising to know that death at a cellular level lacks a widely recognized mathematical definition.

Originally published on Towards AI.

AI hallucinations are a strange and sometimes worrying phenomenon. They happen when an AI, like ChatGPT, generates responses that sound real but are actually wrong or misleading. This issue is especially common in large language models (LLMs), the neural networks that drive these AI tools. They produce sentences that flow well and seem human, but without truly “understanding” the information they’re presenting. So, sometimes, they drift into fiction. For people or companies who rely on AI for correct information, these hallucinations can be a big problem — they break trust and sometimes lead to serious mistakes.

So, why do these models, which seem so advanced, get things so wrong? The reason isn’t only about bad data or training limitations; it goes deeper, into the way these systems are built. AI models operate on probabilities, not concrete understanding, so they occasionally guess — and guess wrong. Interestingly, there’s a historical parallel that helps explain this limitation. Back in 1931, a mathematician named Kurt Gödel made a groundbreaking discovery. He showed that every consistent mathematical system has boundaries — some truths can’t be proven within that system. His findings revealed that even the most rigorous systems have limits, things they just can’t handle.

The search for quantum gravity has gone on for 100 years, but it is not the only unification challenge in physics. Many of us believe that one day there will be a unification theory—a theory that will reconcile many divergent physical theories.

Our new article published in Physica Scripta brings new hope that such a theory exists. It demonstrates that the use of a certain mathematical object called Alena Tensor reconciles various physical theories, including general relativity, electrodynamics, quantum mechanics and continuum mechanics. Will this finally allow scientists to unify descriptions used in physics?

A team of researchers from the University of Cologne, Hasselt University (Belgium) and the University of St Andrews (Scotland) has succeeded in using the quantum mechanical principle of strong light-matter coupling for an optical technology that overcomes the long-standing problem of angular dependence in optical systems.

The study, “Breaking the angular dispersion limit in thin film optics by ultra-strong light-matter coupling,” published in Nature Communications presents ultra-stable thin-film polariton filters that open new avenues in photonics, sensor technology, optical imaging and display technology.

The study at the University of Cologne was led by Professor Dr. Malte Gather, director of the Humboldt Center for Nano-and Biophotonics at the Department of Chemistry and Biochemistry of the Faculty of Mathematics and Natural Sciences.

Science and Technology: Google said its quantum computer, based on a computer chip called Willow, needed less than five minutes to perform a mathematical calculation that one of the world’s most powerful supercomputers could not complete in 10 septillion years, a length of time that exceeds the age of the known universe.

Electronic skins (e-skins) are flexible sensing materials designed to mimic the human skin’s ability to pick up tactile information when touching objects and surfaces. Highly performing e-skins could be used to enhance the capabilities of robots, to create new haptic interfaces and to develop more advanced prosthetics.

In recent years, researchers and engineers have been trying to develop e-skins with individual tactile units (i.e., taxels) that can accurately sense both normal (i.e., perpendicular) and shear (i.e., lateral) forces. While some of these attempts were successful, most existing multi-axis sensors are based on intricate designs or require complex fabrication and calibration processes, which limits their widespread deployment.

Continue reading “Soft e-skin utilizes magnetic fields to independently sense three-axis forces” »

Summary: Human number cognition may be rooted in the putamen, a deep brain structure traditionally associated with movement rather than abstract thought. Neurosurgery patients demonstrated activity in this area while processing numbers as symbols, words, and concepts, suggesting that numerical understanding emerged early in evolution.

Researchers also observed activity in expected areas like the parietal lobe, highlighting how different brain regions collaborate in number processing. These findings could improve surgical outcomes by protecting areas crucial for number cognition and open pathways to enhancing math learning through targeted interventions.

It was 1,229 CE in the monastery of St Sabas, near Jerusalem, and a monk named Johannes Myronas was in need of some parchment. He had evidently been tasked with creating a copy of the Euchologion – an important book of prayer and worship directions for Eastern Orthodox and Byzantine Catholic churches.

The problem was, parchment was expensive and hard to come by. Recycling was the name of the game, and Johannes had just the thing: a 200-year-old manuscript filled with old math notes that nobody was all that interested in anymore. Compared with the Holy Word, there was no contest: he pulled it apart, scraped the old text off, and used the pages for the new book – a technique known as palimpsesting.

You probably know where this is going. In creating his Euchologion, Johannes had – presumably unwittingly – destroyed one of the most valuable relics of Archimedes’s work. Not just some notebook or single treatise, even: the manuscript now known as “Codex C” contained multiple works from the ancient polymath, some of which now exist nowhere else in the world.

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Mathematician Stephen Wolfram has attempted to develop a theory of everything using hypergraphs, which are essentially sets of graphs that can describe space-time. Recently, another mathematician named Jonathan Gorard has used hypergraphs to describe what happens if a black hole accretes matter. He claims that evidence for hypergraphs should be observable in the energy that is emitted during the accretion. Big if true, as they say. Let’s take a look.

Continue reading “This Theory of Everything Actually Makes a Prediction: New Physics in Black Holes” »