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Category: mathematics – Page 10

With their slender tails, human sperm propel themselves through viscous fluids, seemingly in defiance of Newton’s third law of motion, according to a recent study that characterizes the motion of these sex cells and single-celled algae.

Kenta Ishimoto, a mathematical scientist at Kyoto University, and colleagues investigated these non-reciprocal interactions in sperm and other microscopic biological swimmers, to figure out how they slither through substances that should, in theory, resist their movement.

When Newton conceived his now-famed laws of motion in 1686, he sought to explain the relationship between a physical object and the forces acting upon it with a few neat principles that, it turns out, don’t necessarily apply to microscopic cells wriggling through sticky fluids.

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White holes, the theoretical opposites of black holes, could expel matter instead of absorbing it. Unlike black holes, whose event horizon traps everything, white holes would prevent anything from entering. While no white holes have been observed, they remain an intriguing mathematical possibility. Some astrophysicists have speculated that gamma ray bursts could be linked to white holes, and even the Big Bang might be explained by a massive white hole. Although the second law of thermodynamics presents a challenge, studying these singularities could revolutionize our understanding of space-time and cosmic evolution.

After reading the article, Harry gained more than 724 upvotes with this comment: “It amazes me how Einstein’s theory and equations branched off into so many other theoretical phenomena. Legend legacy.”

Black holes may well be the most intriguing enigmas in the Universe. Believed to be the collapsed remnants of dead stars, these objects are renowned for one characteristic in particular – anything that goes in never comes out.

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The standard model of fundamental particles and interactions has now been in place for about a half-century. It has successfully passed experimental test after experimental test at particle accelerators. However, many of the model’s features are poorly understood, and it is now clear that standard-model particles only compose about 5% of the observed energy density of the Universe. This situation naturally encourages researchers to look for new particles and interactions that fall outside this model. One way to perform this search is to prepare a gas of polarized atoms and to look for changes in this polarization that might come from new physics. Haowen Su from the University of Science and Technology of China and colleagues have used two separated samples of polarized xenon gas to probe spin-dependent interactions [1] (Fig. 1). The results place constraints on axions—a candidate for dark matter—in a theoretically favored mass range called the axion window.

Searches for new spin-dependent interactions have exploded over the past decade. Special relativity and quantum mechanics tightly constrain the mathematical form for such interactions, with the main adjustable parameters being the coupling strength and the spatial range. Since the form of these interactions is generic across many models, it is possible to conduct experimental searches for new interaction signatures, even in the absence of a specific theory for beyond-standard-model physics.

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True humility is rare today. It takes courage and a strong stance. It’s the story of Grigori Perelman, who proved the Poincaré conjecture — the only one of the seven Millennium Prize Problems solved by humanity. 1️⃣ In 1990s, Perelman worked at UC Berkeley. Top universities tried to hire him. A hiring committee at Stanford asked him for a C.V. to include with requests for letters of recommendation. But Perelman said: “If they know my work, they don’t need my C.V. If they need my C.V., they don’t know my work.” he received several job offers. But he declined them all. 2️⃣ In 2002–2003, he posted three manuscripts on arXiv where he solved the Poincare problem. On a PREPRINT server. Not in a journal! He did not care about publishing them in Nature. He did not care about getting them peer reviewed. He just wanted to make his work publicly available. Several leading math groups immediately started checking his proof. 3️⃣ In 2006, he was awarded a Fields Medal for his work on the Ricci flow and Poincare conjecture. But Perelman declined it: “[The prize] was completely irrelevant for me. Everybody understood that if the proof is correct, then no other recognition is needed.” He did not attend the ceremony. He was the only person to have ever declined the prize. 4️⃣ In 2010, Perelman was awarded a Millennium Prize ($1,000,000). He did not attend a ceremony in Paris as well. He considered the decision of the Clay Institute unfair because he wanted to share the prize with Richard Hamilton (who had a big influence on Perelman in 1990s). “The main reason is my disagreement with the organized mathematical community. I don’t like their decisions, I consider them UNJUST.” ❗️Why I am writing all this? Because: There’s no fairness in academia. It’s unjust and often illogical. It’s full of competition and unkindness. Perelman was very sensitive to it. So, he left mathematics… IF we don’t want to lose brilliant minds like this… IF we want our kids to love science as they grow up… Then we should focus on making it a better place. Less pressure on tenure track professors. No pursuit of metrics. No emphasis on awards. More mentorship and quality research. We need it. #science #research #engineering #mathematics #scienceandtechnology

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In a study published in Physical Review Letters, researchers at the Center for Computational Quantum Physics (CCQ) at the Flatiron Institute have revealed that the quantum problem they solved, which involved a specific two-dimensional quantum system of flipping magnets, exhibits a behavior known as confinement. This problem explains why they defeated the quantum computer in its own game. Only one-dimensional systems had previously exhibited this behavior in quantum condensed matter physics.

The researchers revealed earlier this year that they had completely surpassed a quantum computer at a task that some believed could only be completed by quantum computers by using a classical computer and complex mathematical models.

According to lead author Joseph Tindall, a research fellow at the CCQ, this surprising discovery is giving researchers a framework for evaluating novel quantum simulations and aiding in their understanding of the boundary between quantum and classical computers’ capabilities.

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From the article:

Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve.

The results are a sweeping, game-changing math proof that was decades in the making.

Yale’s Sam Raskin has solved a major portion of a math question that could lead to a translation theory for some areas of math.

Continue reading “A geometry masterpiece: Yale prof solves part of math’s ‘Rosetta Stone’” | >

On this day in 1992, the Vatican admitted that Galileo was correct in believing that the earth went around the sun.

2. In the first place, I wish to congratulate the Pontifical Academy of Sciences for having chosen to deal, in its plenary session, with a problem of great importance and great relevance today: the problem of ‘the emergence of complexity in mathematics, physics, chemistry and biology’

The emergence of the subject of complexity probably marks in the history of the natural sciences a stage as important as the stage which bears relation to the name of Galileo, when a univocal model of order seemed to be obvious. Complexity indicates precisely that, in order to account for the rich variety of reality, we must have recourse to a number of different models.

This realisation poses a question which concerns scientists, philosophers and theologians: how are we to reconcile the explanation of the world – beginning with the level of elementary entities and phenomena – with the recognition of the fact that ‘the whole is more than the sum of its parts’?

Continue reading “1992, 31 October” | >

Dr. Sanjeev Namjoshi, a machine learning engineer who recently submitted a book on Active Inference to MIT Press, discusses the theoretical foundations and practical applications of Active Inference, the Free Energy Principle (FEP), and Bayesian mechanics. He explains how these frameworks describe how biological and artificial systems maintain stability by minimizing uncertainty about their environment.

Namjoshi traces the evolution of these fields from early 2000s neuroscience research to current developments, highlighting how Active Inference provides a unified framework for perception and action through variational free energy minimization. He contrasts this with traditional machine learning approaches, emphasizing Active Inference’s natural capacity for exploration and curiosity through epistemic value.

The discussion covers key technical concepts like Markov blankets.
generative models, and the distinction between continuous and discrete implementations. Namjoshi explains how Active Inference moved from continuous state-space models (2003−2013) to discrete formulations (2015-present) to better handle planning problems.

He sees Active Inference as being at a similar stage to deep learning in the early 2000s — poised for significant breakthroughs but requiring better tools and wider adoption. While acknowledging current computational challenges, he emphasizes Active Inference’s potential advantages over reinforcement learning, particularly its principled approach to exploration and planning.

Continue reading “The Hidden Math Behind All Living Systems” | >

Researchers explore an intriguing phenomenon in quantum systems, drawing inspiration from a recent quantum computing experiment.

Earlier this year, researchers at the Flatiron Institute’s Center for Computational Quantum Physics (CCQ) announced that they had successfully used a classical computer and sophisticated mathematical models to thoroughly outperform a quantum computer on a task that some thought only quantum computers could solve.

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