For Context: OpenAI has recently introduced two new AI models, o3 and o3-mini, designed to enhance reasoning capabilities in complex tasks such as advanced mathematics, science, and coding. These models represent a significant advancement over their predecessor, o1, which was released in September 2024.
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The Riemann Hypothesis is an open problem in maths which â if proved correct â would show us a pattern in prime numbers. The zeta function, a central part of the hypothesis, has been linked to quantum mechanics, and recently a group of physicists linked it to gravitational equations associated with black holes. What does this mean, exactly? Letâs take a look.
Paper: https://link.springer.com/article/10⊠mugs, posters and more: â https://sabines-store.dashery.com/ đ Support me on Donorbox â https://donorbox.org/swtg đ Transcript with links to references on Patreon â / sabine đ Transcripts and written news on Substack â https://sciencewtg.substack.com/ đ© Free weekly science newsletter â https://sabinehossenfelder.com/newsle⊠đ Audio only podcast â https://open.spotify.com/show/0MkNfXl⊠đ Join this channel to get access to perks â
/ @sabinehossenfelder đ Buy my book â https://amzn.to/3HSAWJW #science #sciencenews #physics #maths The Riemann hypothesis is a significant open problem in mathematics, deeply intertwined with number theory and its implications for physics. This video explores how the riemann zeta function, a central element of the hypothesis, connects to fundamental concepts like black hole physics and quantum gravity. Discover the ongoing mathematical research that seeks to solve this enduring mysteryâŠ
đT-shirts, mugs, posters and more: â https://sabines-store.dashery.com/
đ Support me on Donorbox â https://donorbox.org/swtg.
đ Transcript with links to references on Patreon â / sabine.
đ Transcripts and written news on Substack â https://sciencewtg.substack.com/
đ© Free weekly science newsletter â https://sabinehossenfelder.com/newsleâŠ
đ Audio only podcast â https://open.spotify.com/show/0MkNfXlâŠ
đ Join this channel to get access to perks â
/ @sabinehossenfelder.
đ Buy my book â https://amzn.to/3HSAWJW
#science #sciencenews #physics #maths.
The Riemann hypothesis is a significant open problem in mathematics, deeply intertwined with number theory and its implications for physics. This video explores how the riemann zeta function, a central element of the hypothesis, connects to fundamental concepts like black hole physics and quantum gravity. Discover the ongoing mathematical research that seeks to solve this enduring mystery.
Isolating the first spark of life on Earth is a matter of biology, geology, and chemistryâbut itâs also an amazing math problem. At least, thatâs how Varun Varanasi viewed it when he was a Yale undergraduate. The question, in a nutshell, is this: How did the primordial soup of interacting molecules on the Earthâs surface billions of years ago transform itself from complete chaos to an organized system of self-sustaining, reproducing chemicals? Did this occur gradually over millions of years, or was it abrupt?
An international team of scientists, including researchers from Loughborough University, has developed a method to dramatically speed up the discovery and design of advanced materials. The study, published in Physical Review Letters, shows how the new approach can map complex phase diagrams in as little as a dayârather than weeks or monthsâand pinpoint where important structures, including crystals and quasicrystals, are likely to form.
The method will enable scientists to âscout aheadâ and identify where promising structures are likely to form and the conditions needed to create them, rather than using a trial-and-error approach. It could help accelerate the development of advanced materials and technologies that harness the unique properties of quasicrystal structures.
âOur approach is a dayâs work for an expertâitâs much faster,â said Professor Andrew Archer, an expert in applied mathematics and theoretical physics at Loughborough University and one of the paperâs authors.
What if creativity wasnât magicâbut math?
In this video, we explore the mathematics of creativity through psychology, philosophy, and science. From Dean Keith Simontonâs law of large numbers, Margaret Bodenâs theory of combinational creativity, Zipfâs Law, Malcolm Gladwellâs 10,000-hour curve, and even cellular automataâwe break down how imagination follows hidden equations.
Whether youâre a student, teacher, scientist, engineer, or philosopher, this video will change how you think about art, science, and human innovation.
Chapters:
00:00 â Intro: Is Creativity Random?
00:34 â The Law of Large Numbers
01:42 â Zipfâs Law of Ideas
02:33 â Combinational Creativity (Boden)
03:15 â Time & Growth (Gladwell)
03:58 â Edge of Chaos (Complexity Theory)
04:48 â The Formula for Creativity.
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#creativity #mathematics #philosophy #science #innovation #abstractthinking #complexity #psychology #ideas #inspiration #bigthink #veritasium #numberphile #vsauce #kurzgesagt #education #learning #sciencetok #philosophytok #tech #artandscience #genius #edgeofchaos #combinatorialcreativity #mathandcreativity #theory #thinking #intelligence #knowledge
âIt is impossible to be a mathematician without being a poet in soul.â-Sofia Kovalevskaya
We donât often think of math as something thatâs âdangerousâ or âforbiddenâ; after all, what could be so dangerous about numbers? Russian-born Sofia Kovalevskaya was told at numerous points during her life that she had to stop studying math, that girls werenât good enough, they werenât allowed to go to school, or teach classes, edit magazines or win awards. Sofia Kovalevskaya never gave in to the couldnâtâs or wouldnâtâs. She fought time and again for her right to continue learning and teaching, eventually becoming one of the most celebrated mathematicians of her century and the first woman professor of a northern European University. Today, we celebrate Sofia and all the young mathematicians who overcome great odds!
When Sofia Kovalevskaya was a little girl in the early 1850âs, her room wasnât wallpapered with flowers or meadowscapes, it was covered in pages and pages of math lecture not es. She would stare at the pages filled with differential and integral analysis, and while she didnât understand exactly what she saw, Sofia saw beauty in the calculations.
Crystals, bacterial colonies, flame fronts: the growth of surfaces was first described in the 1980s by the KardarâParisiâZhang equation. Since then, it has been regarded as a fundamental model in physics, with implications for mathematics, biology, and computer science.
Nowâ40 years laterâa WĂŒrzburg-based research team from the Cluster of Excellence ctd.qmat has achieved the first experimental demonstration of KPZ behavior on 2D surfaces in space and time.
This was made possible by sophisticated materials engineering and a bold experimental approach: researchers injected polaritonsâhybrid particles composed of light and matterâinto the material. The results have been published in Science.
Can a wall get stronger the more it breaks, and greener the more it stands? Swiss scientists say buildings are about to start breathing and devouring carbon, and the concrete status quo will not like the math.
From a Zurich lab comes a building skin that inhales carbon, knits its own cracks and grows sturdier with time. Researchers at ETH Zurich embedded photosynthetic cyanobacteria in a 3D printed hydrogel, creating a living material that draws down COâ and strengthens over time, its chlorophyll tinting it green. Across 400 days of testing, a prototype matched the yearly uptake of a 20-year-old pine, pulling in up to 18 kilograms of COâ, while each gram of the base material fixes about 26 milligrams. Detailed in Nature Communications on April 6, 2026 and co-authored by Mark Tibbitt, the work points to facades that do carbon duty as part of everyday architecture.
Some breakthroughs feel both surprising and oddly familiar, like rediscovering a tool nature kept in plain sight. Swiss scientists have blended biology with architecture to shape a new kind of material that lives with its surroundings. It repairs small cracks, it sips CO2 from the air, and it quietly strengthens with time. The promise is simple, and bold: buildings that help clean the sky.
David J. Silvester, a mathematics professor at the University of Manchester, has developed a novel machine-learning method to detect sudden changes in fluid behavior, improving speed and the cost of identifying these instabilities and overcoming one of the major obstacles faced when using machine learning to simulate physical systems. The findings are published in the Journal of Computational Physics.
Computational simulations of mathematical models of fluid flow are essential for everyday applications ranging from predicting the weather to the assessment of nuclear reactor safety. The advent of this simulation capability over the past 50 years has revolutionized the development of fuel-efficient airplanes, and sail configurations on racing yachts can now be optimized in real time, providing the marginal gains needed to win races in the Americaâs Cup.
Optimized aerodynamics means that modern day cyclists can ride faster, golf balls fly further and Olympic swimmers consistently set world records. Computational fluid dynamics also enables the modeling of the flow of blood in the human heart, making the provision of patient-specific surgery possible.
For years, Rutgers physicist David Shih solved Rubikâs Cubes with his children, twisting the colorful squares until the scrambled puzzle returned to order. He didnât expect the toy to connect to his research, but recently he realized the logic behind the puzzle was exactly what he needed to solve a problem involving particle physics.
That idea led to a new artificial intelligence (AI) method that can simplify some of the extremely complex equations used in particle physics. Shih described the method in a study posted to the arXiv preprint server, a widely used site where scientists share new research.
âIn reaching our solutions, we found that an analogy between mathematical simplification and solving Rubikâs Cubes was key,â said Shih, a professor in the Department of Physics and Astronomy at the Rutgers School of Arts and Sciences. âBoth can be viewed as scrambling and unscrambling problems.â