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Category: mathematics – Page 5

‘Silly sprinklers’ put in reverse to further unravel decades-old physics puzzle

Each summer, lawns are marked by a familiar addition: “silly sprinklers,” whose loops and spirals spew water in creative ways. While seemingly frivolous in their construction, a team of mathematicians has used their design to address a long-standing mystery surrounding the laws of physics.

For decades, scientists have been trying to solve Feynman’s Sprinkler Problem: How does a sprinkler running in reverse—in which the water flows into the device rather than out of it—work? Through a series of experiments on custom-designed sprinklers with different shapes, the researchers arrived at a clear answer and, more generally, determined how flowing fluids exert forces and move structures.

“This work provides the experimental answer for Feynman’s Sprinkler Problem by showing, across several sprinkler types, how the angular momentum of water flows drives sprinklers’ rotation,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute School of Mathematics, Computing, and Data Science and the senior author of the paper, which appears in the journal Proceedings of the National Academy of Sciences.

Sia Performs “Unstoppable” To Close the 2025 Breakthrough Prize Ceremony

Multi-platinum recording artist Sia closed the Breakthrough Prize ceremony with an inspiring rendition of “Unstoppable” as all prize laureates returned to the stage to a standing ovation.
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The eleventh Breakthrough Prize awards celebrated outstanding scientific achievements, honoring scientists driving remarkable discoveries in gene editing, human diseases, the search for the fundamental laws of the Universe and pure mathematics. Held at the Barker Barker Hangar in Santa Monica, CA, presentations were given by Christina Aguilera, Drew Barrymore, MrBeast, Lily Collins, Vin Diesel, Jodie Foster, Gal Gadot, Salma Hayek Pinault, Ke Huy Quan, Gayle King, Edward Norton, Gwyneth Paltrow, Seth Rogen, Lauren Sanchez, Jeremy Strong, will.i.am, and more. With live performances by Katy Perry and Sia. Continued at https://breakthroughprize.org/News/92.

Full show: • 2025 Breakthrough Prize Ceremony: Full Show.

https://breakthroughprize.org

‘Complex numbers are not needed for quantum mechanics’: Physicists develop quantum model that uses only ‘real’ numbers for first time ever

For the first time, physicists have built a working version of quantum mechanics without complex numbers — numbers that have been considered essential to the theory for nearly a century.

Complex numbers combine a regular “real” number with an “imaginary” one — a multiple of the square root of-1, represented by the symbol i — into a single value, like 3 + 4i. The square root of-1 doesn’t correspond to any quantity you could count or measure directly (you can’t have negative one apple, for instance), which is why mathematicians call it imaginary.

Is AI making us stupid?

Not exactly—but how we use it matters.

A new Trends in Cognitive Sciences perspective argues that AI doesn’t inherently erode human intelligence. Instead, it highlights a well-known principle in cognitive psychology: cognitive offloading.

When we let AI perform tasks that require reasoning, writing, memory, or problem-solving, we reduce the amount of mental practice our brains receive. Like physical exercise, cognitive skills strengthen through use and weaken through disuse.

Skills: learned abilities such as writing, mathematical reasoning, diagnosis, or programming. These are most vulnerable if AI consistently replaces the learning process.

Basic cognitive abilities: foundational functions like working memory, attention, and executive control. Current evidence suggests these may be more resistant to decline, although more research is needed.

The key message isn’t that AI makes people “stupid.” Rather: AI can improve immediate performance. Overreliance may reduce long-term learning and skill retention.

AI is most beneficial when it augments human thinking instead of replacing it. This fits with decades of neuroscience showing that practice drives neuroplasticity. The brain adapts to the cognitive demands we place on it. If.

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New test certifies quantum measurements that simpler methods cannot mimic

Proving that one quantum measurement is more powerful than another has long been difficult. Physicists from Heinrich Heine University Düsseldorf, Lund University and the University of Innsbruck have now developed and demonstrated a simple technique to certify that a certain class of measurements has properties that cannot be mimicked by simpler means. Their paper is published in the journal PRX Quantum.

Measurements are central to all quantum technologies. They are said to “collapse” the quantum state they act on, destroying its quantum properties and serving as the bridge to the classical world. Curiously, quantum mechanics allows for measurements that are more general than the ones we can directly associate with classical properties of a system.

These generalized measurements, or POVMs, short for Positive Operator Valued Measures, are not just a mathematical curiosity. They are known to improve performance in tasks like distinguishing between quantum states that would otherwise be indistinguishable, extracting more information from quantum sensors and securing quantum communication.

Set theory | Two maths problem

Here I discuss definition of set, subset, proper subset, de Morgan’s law, Associative law, Cartesian product with theory and solve two maths problem.
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A Widening Anomaly Strains the Standard Model

Does a new measurement of a rare decay of the neutral B meson portend new physics?

In particle physics, ten years is a long time to sit with a puzzle. Since 2013, measurements of a rare decay—a neutral B meson (B0) transforming into an excited kaon (K*0) and a muon–antimuon pair (µ+µ –)—have stubbornly refused to match the predictions of the standard model, the theory that describes all known particles and forces [1]. Small enough to be dismissed at first as a statistical fluctuation, the pattern of discrepancies has grown with each new dataset into one of the most tantalizing hints of new physics in experimental particle physics. Now the LHCb Collaboration at CERN in Switzerland has published its most comprehensive analysis of the decay to date [2]. The result is clear: The anomaly persists. Encouragingly, the theoretical and experimental tools to understand it have never been sharper.

Within the mathematical framework of the standard model, the decay in question, B0 → K*0µ+µ–, can occur only through so-called higher-order electroweak loop diagrams in which a bottom, or b, quark transforms into a strange, or s, quark [3]. As a result, the decay is extraordinarily rare. In every million B-meson decays of all kinds, you can expect to find only one. That rarity makes the decay valuable: It could bear measurable imprints of particles beyond the standard model that contribute to the same loop processes but have so far escaped detection because they are too heavy.

George Dyson on Turing’s Cathedral: In Wildness Is The Preservation Of The World

Fourteen years ago, I sat down with George Dyson to talk about “Turing’s Cathedral.”

We talked about the machines that were coming. Now they are here.

Dyson watched the digital revolution get built from the inside. His father was Freeman Dyson. Einstein’s secretary was his babysitter. He grew up at the Institute for Advanced Study in Princeton, playing in the halls where Turing’s ideas became von Neumann’s machines.

He gave me a line I still cannot shake:

“There is no way to completely govern the digital universe. It will always be a wildness, not a bureaucracy or a national park.”

Read it again. Then look at every #AI governance debate happening right now.

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