John Nash was born on June 13, 1928, in Bluefield, West Virginia, a former coal town nestled deep in the Appalachian Mountains. As a young boy, Nash was solitary, bookish, and introverted. His father, John Sr., was a quiet engineer with an incisive mind. His mother, Virginia, also intelligent, was a former teacher who had large dreams for her son, pushing him to read at four, learn Latin, and skip a grade at school.
The first hint of John Nash’s math talent came in fourth grade, when a teacher told Virginia that the boy couldn’t do the math. Virginia laughed, well aware that her son was going down his own path to solve the simple problems. In high school, John solved his teachers’ clunky proofs in just a few elegant steps. He was one of ten nationally awarded winners of the George Westinghose Award, which provided him with a full scholarship to the Carnegie Institute of Technology. He hopped from engineering to chemistry before discovering his passion: mathematics.
He was accepted into Princeton University, which at the time was to mathematicians what Detroit was, and still is, to cars. Nash first wowed his peers with an elegantly playable board game, which his peers dubbed “Nash,” but later reached the market as Hex. He then absorbed himself in one of the sexiest math fields of the day, game theory, which described strategies in competition, whether in card games or business. His deceptively simple doctoral thesis would later re-orient the field of economics, although no one, not even Nash, predicted its potential.
Most people wouldn’t think that it would take rigorous mathematical proof to show how many folds it takes to make a donut shape out of paper. Yet, no one could quite figure it out until recently.
In a new paper, published in Proceedings of the National Academy of Sciences, mathematician Richard Evan Schwartz provides detailed proof of where the line is drawn when it comes to the fewest folds required to construct a torus—the proper name for the shape of a donut—from a piece of paper.
The planar Hall effect is a tabletop diagnostic tool for special quantum properties useful in basic research and technological applications. Or so it was thought, because careful calculation by Kobe University researchers clarifies the conditions under which this effect may also appear in classical materials. This makes the diagnostic more meaningful and enables more purposeful design.
In the hunt for materials with properties that are useful for quantum computing or spintronics, researchers have used the “planar Hall effect” as a tabletop diagnostic tool: The researchers send a current through a thin, flat sample and observe whether an electric voltage is produced in response to a magnetic field in the same plane as the sample.
If it is, the pattern of how the voltage responds to rotating the magnetic field in the plane of the sample tells researchers about the properties of the material.
In 1937, a young graduate student named Claude Shannon submitted a master’s thesis with an unassuming title: “A Symbolic Analysis of Relay and Switching Circuits.”
The utilization of the binary properties of electrical switches to perform logic functions is the basic concept that underlies all electronic digital computer designs. Shannon’s thesis became the foundation of practical digital circuit design when it became widely known among the electrical engineering community during and after World War II. At the time, the methods employed to design logic circuits (for example, contemporary Konrad Zuse’s Z1) were ad hoc in nature and lacked the theoretical discipline that Shannon’s paper supplied to later projects.
Shannon’s work also differed significantly in its approach and theoretical framework compared to the work of Akira Nakashima. Whereas Shannon’s approach and framework was abstract and based on mathematics, Nakashima tried to extend the existent circuit theory of the time to deal with relay circuits, and was reluctant to accept the mathematical and abstract model, favoring a grounded approach. [ 6 ] Shannon’s ideas broke new ground, with his abstract and modern approach dominating modern-day electrical engineering. [ 6 ].
How ambitious should you be? Folk wisdom offers conflicting advice: “Shoot for the moon,” but also, “Don’t let the perfect be the enemy of the good.” A new study by researchers at the University of Wyoming, Stanford University and the University of Colorado-Boulder used a mathematical model to show that ambition lies in the middle—above average but finite.
“Conventional wisdom tells people not to settle, but also not to let the perfect be the enemy of the good,” says lead author Kath Landgren, a postdoctoral scholar at Stanford’s Doerr School of Sustainability. “We wanted to see whether the math actually supports that intuition. It does, with some interesting twists.”
Roger Penrose and Brian Cox discuss how Roger got interested in physics, the Big Bang, and the role of beauty in mathematics.
Do you agree with Roger’s thoughts on string theory?
With a free trial, you can watch the full conversation NOW at https://iai.tv/video/our-future-theor… the Big Bang to the fabric of spacetime and the nature of consciousness, our core scientific assumptions frame how we understand and perceive reality. But there are many challenges to our current understanding. What if the very foundations of our theories are flawed? Should we reconsider our understanding? And how radically might our view of the universe have to change? Join Roger Penrose, Nobel Prize Laureate and winner of the Wolf prize, in collaboration with Stephen Hawking, with legendary physicist and science communicator, Brian Cox, to explore whether the flaws in our current theories are at some fundamental level insurmountable, or whether they can be extended or changed to overcome these challenges. #physics #cosmology #bigbang Awarded the 2020 Nobel Prize in Physics for his work on black holes, Roger Penrose is a world-renowned mathematician and physicist. In recent years, he has investigated the relationship between physics and the mind, famously arguing that quantum mechanics plays an essential role in solving the mysteries of human consciousness. Penrose has made numerous appearances on media such as BBC, Closer to Truth, and The Joe Rogan Experience. In 1994, he was knighted for his services to science. Famed for his poetic take on the cosmos, physicist and broadcaster Brian Cox has become one of the world’s most recognizable voices in science communication. A former musician turned particle physicist, Cox has played a key role in major experiments at CERN and the Large Hadron Collider, while also captivating millions through BBC series such as Wonders of the Universe, The Planets, and Forces of Nature. Cox has been showered with praise for his contributions, appointed Commander of the Order of the British Empire (CBE), and is the recipient of the Institute of Physics Kelvin Medal and the Michael Faraday Prize. Beyond his work as a Royal Society professor of physics at the University of Manchester, Cox advocates for public scientific literacy and political responsibility in science funding. His style blends rigorous physics with a deep sense of awe — bringing relativity, entropy, and quantum theory into living rooms around the globe. His rare ability to fuse clarity with wonder has earned global acclaim. The Institute of Art and Ideas features videos and articles from cutting edge thinkers discussing the ideas that are shaping the world, from metaphysics to string theory, technology to democracy, aesthetics to genetics. Subscribe today! https://iai.tv/subscribe?utm_source=Y… 0:00 Intro 0:44 Brian Cox on how Roger Penrose inspired him 1:39 — Beauty in mathematics 3:00 — How Roger struggled with maths at school 6:51 — How Roger got interested in physics 9:27 — What theory is best for explaining the beginning of the universe? 12:12 — A key new discovery in cosmology 18:44 — The big bang is not quantum mechanical For debates and talks: https://iai.tv For articles: https://iai.tv/articles For courses: https://iai.tv/iai-academy/courses.
From the Big Bang to the fabric of spacetime and the nature of consciousness, our core scientific assumptions frame how we understand and perceive reality. But there are many challenges to our current understanding. What if the very foundations of our theories are flawed? Should we reconsider our understanding? And how radically might our view of the universe have to change? Join Roger Penrose, Nobel Prize Laureate and winner of the Wolf prize, in collaboration with Stephen Hawking, with legendary physicist and science communicator, Brian Cox, to explore whether the flaws in our current theories are at some fundamental level insurmountable, or whether they can be extended or changed to overcome these challenges.
#physics #cosmology #bigbang.
Awarded the 2020 Nobel Prize in Physics for his work on black holes, Roger Penrose is a world-renowned mathematician and physicist. In recent years, he has investigated the relationship between physics and the mind, famously arguing that quantum mechanics plays an essential role in solving the mysteries of human consciousness.
From that insight, Dirac built an entirely new formulation of the theory using what he called “q-numbers” (quantum numbers)—abstract quantities that don’t commute. He independently rediscovered aspects of Hilbert’s operator theory, though he preferred his own algebraic route because he found mathematicians’ obsession with convergence and existence theorems unappealing.
Mathematicians are challenging the idea that dark energy is responsible for the accelerating expansion of the universe. In a new paper published in Proceedings of the Royal Society A, mathematicians from the University of California, Davis, provide mathematical proof that instabilities inherent in the Einstein-Euler equations imply that the current model of the expanding universe is not viable.
The Einstein-Euler equations are a union of general relativity and fluid dynamics equations used to model astronomical phenomena such as galaxies, black holes, and cosmic expansion.
The research directly challenges the Lambda-cold dark matter model, the standard cosmological model of the Big Bang.
Google DeepMind’s Demis Hassabis says humanity may already be standing in the foothills of the singularity. AI agents are now coding, researching, planning, paying, helping with science, and cutting real work from days to minutes. The big question is no longer whether AI is perfect. It’s whether imperfect AI has already become useful enough to speed up everything around it.
📌 What You’ll See: Google DeepMind’s warning that we are entering the foothills of the singularity. SOURCE: https://www.axios.com/2026/05/26/deep… new Gemini for Science tools built to speed up scientific discovery SOURCE: https://blog.google/innovation-and-ai… AWS letting autonomous AI agents make payments and complete transactions SOURCE: https://aws.amazon.com/about-aws/what… AxiomProver helping prove new math results in Lean and Mathlib SOURCE: https://arxiv.org/abs/2602.05090 Biohub’s new world model of protein biology trained across billions of sequences SOURCE: https://biohub.ai/esm/protein ARC-AGI-3 showing the huge gap between today’s frontier AI and human reasoning SOURCE: https://aiforautomation.io/news/2026-… 🚨 Why It Matters This is bigger than another AI model update. Google DeepMind is now openly talking about the singularity, while AI agents are already starting to speed up coding, science, business, and research. Some experts think AGI may be closer than expected, while others say current AI still lacks true intelligence. Either way, the AI race is shifting fast from chatbots into agents that can plan, act, build, discover, and change real workflows. #google #singularity #ai. Google’s new Gemini for Science tools built to speed up scientific discovery. SOURCE: https://blog.google/innovation-and-ai… AWS letting autonomous AI agents make payments and complete transactions. SOURCE: https://aws.amazon.com/about-aws/what… AxiomProver helping prove new math results in Lean and Mathlib. SOURCE: https://arxiv.org/abs/2602.05090 Biohub’s new world model of protein biology trained across billions of sequences. SOURCE: https://biohub.ai/esm/protein. ARC-AGI-3 showing the huge gap between today’s frontier AI and human reasoning. SOURCE: https://aiforautomation.io/news/2026-…
🚨 Why It Matters. This is bigger than another AI model update. Google DeepMind is now openly talking about the singularity, while AI agents are already starting to speed up coding, science, business, and research. Some experts think AGI may be closer than expected, while others say current AI still lacks true intelligence. Either way, the AI race is shifting fast from chatbots into agents that can plan, act, build, discover, and change real workflows.
A study by researchers at The University of Manchester, carried out alongside the Universities of Melbourne and Copenhagen, could hold the key to understanding the causes of long-term health problems, such as infertility and ovarian cancer.
The study, published in PRX Life, used a combination of high-resolution imaging, flow measurements, and mathematical modeling to examine fluid flows around corals that are driven by cilia—densely packed tiny hairs on the coral’s surface. The collective beating of the cilia contributes to the movement of fluid around the surface of the coral, regulating the animal’s immediate environment through the transport of particles such as oxygen.
The researchers found that heterogeneity in ciliary orientation —small variations in the direction individual cilia beat—can significantly boost transport efficiency. For substances that diffuse slowly through the fluid, this natural variability increased particle transport by more than 50% compared to perfectly aligned cilia. This contrasts with other biological systems, highlighting how coral cilia are uniquely adapted to their environment.
