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Category: mathematics

Quantum Entangles the Heavens

As the United States, Europe, and China compete to shape the future of the Earth-Moon corridor, strategic advantage will depend not only on launch capacity or lunar infrastructure, but also on advances in quantum technologies. Just as secure systems are critical on Earth, satellites and space-based systems underpin high-value, high-impact operations from financial transactions and navigation to scientific discovery and classified military missions.

Quantum technologies, which enable new levels of speed, sensitivity, and security, are emerging as critical tools to improve existing extraterrestrial systems. Modern digital communications are secured by encryption built on math problems that are extremely difficult for regular computers to solve, but that sufficiently advanced quantum computers could eventually crack. Quantum communications technologies could add a new layer of protection by making it easier to detect when someone is trying to intercept sensitive information. Quantum sensors can measure position and time with an accuracy that GPS only approximates. Lastly, quantum computers could unlock new capabilities beyond current computational limits, from designing advanced materials to optimizing increasingly complex satellite networks.

Countries are racing to match their space and quantum ambitions with national strategies. The White House is reportedly drafting an executive order to strengthen US competitiveness in quantum technologies. The rumored draft directs multiple US government bodies, including NASA, to develop a five-year roadmap to expand quantum sensing and networking capabilities. The EU’s 2025 Quantum Europe Strategy highlights “Space and Dual-Use Quantum Technologies” as one of its five strategic focuses, and China’s 15th Five-Year Plan has called for expanding the country’s ground-to-space quantum communications network.

A Token of Our Imagination: The Invisible Economy Powering GenAI

Ever wonder what actually happens inside the AI after you hit “Enter”?

You type a prompt into your favorite generative AI, and within seconds, your screen fills with exactly what you asked for—whether it’s a quarterly report or a cinematic image of a cyberpunk golden retriever. It feels like absolute magic.

But behind that seamless curtain lies a bustling, microscopic economy running entirely on a digital currency you’ve probably heard of but might not fully understand: the token.

Most of us only ever see the input and the output. We don’t see the internal cash register ringing, the mathematical gymnastics, or the sprawling “assembly line” churning through billions of calculations.

What actually happens between the moment you hit send and the moment your final masterpiece appears? In my newest blog post, I peel back the curtain to trace the fascinating journey of an AI token.

I break down this invisible economy—from the “toll booth” of the input phase to the heavy lifting of the output phase—and show you exactly how the machine balances the books.

Continue reading “A Token of Our Imagination: The Invisible Economy Powering GenAI” | >

AI Is Now Improving Itself

In 1965, a mathematician who worked alongside Alan Turing wrote a single
paragraph that has haunted AI research ever since. He predicted that one
day, a machine would learn to improve itself, and that everything after
that point would change.

Sixty years later, that loop is starting to close.

In this video, we trace how AI got here: from I.J. Good’s 1965 prediction.
to AlphaGo Zero teaching itself Go in 72 hours, to AlphaEvolve cracking a
math problem that had stood unbeaten for 56 years, and then quietly
speeding up the training of the very model that runs it. We look at the
data behind the trend (autonomous AI task length is doubling every 7
months), the walls AI keeps running into (compute, data, energy), and what
the people building this technology are actually saying about how close
we are.

This video is an honest look at what \.

Small talk shapes big trends: Physics predicts how language patterns spread

A new model to predict how language changes over time has been developed by a statistical physicist at the University of Portsmouth. The model is a step towards understanding the “statistical physics of language,” a scientific theory which borrows ideas from the physics of interacting particles to explain how words, accents, and dialects spread, shift, and disappear across regions and generations, and how they might change in future. The research is published in the journal Physical Review E.

James Burridge, Professor of Probability and Statistical Physics, from the University’s School of Mathematics and Physics, said, Just as meteorologists use mathematical models to forecast tomorrow’s weather, the same kind of thinking can be applied to language.

Where you are affects how you speak and if you map how people use certain words, you see clear geographic patterns—just like a weather map. However, the physics of language is closer to crystals and magnets than the atmosphere.

Mathematical framework solves asteroid route planning exactly for first time

A new publication from Bielefeld University sets a benchmark in optimization research. Together with an international team, Professor Michael Römer from the Faculty of Business Administration and Economics has developed a mathematical framework that solves a complex problem from space logistics exactly for the first time: the optimal planning of a route to visit several asteroids under conditions that are as close to reality as possible. The study is published in the INFORMS Journal on Computing.

At the center of the research is the so-called Asteroid Routing Problem. It addresses the question: In what order should a spacecraft visit multiple asteroids if both travel time and fuel consumption are to be minimized? The challenge is that, unlike in classical routing problems, the travel time between destinations is constantly changing because all celestial bodies are in continuous motion.

The idea for the study originated in Bielefeld, sparked by a success in a competition organized by the European Space Agency (ESA). During a research stay in Bielefeld, lead author Isaac Rudich revisited the topic and, together with the team, developed a new solution approach.

What If The Universe Is Math?

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In his essay “The Unreasonable Effectiveness of Mathematics”, the physicist Eugine Wigner said that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious”. This statement was inspired by the observation that so many aspects of the physical world seem to be describable and predictable by mathematical equations to incredible precision especially as quantum phenomena. But quantum phenomena have no subjective qualities and have questionable physicality. They seem to be completely describable by only numbers, and their behavior precisely defined by equations. In a sense, the quantum world is made of math. So does that mean the universe is made of math too? If you believe the Mathematical Universe Hypothesis then yes. And so are you.

#space #universe #maths.

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AI tackles one of math’s most brutal problems: Inverse PDEs

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for understanding the natural world.

The advance, which the researchers call “Mollifier Layers,” could benefit fields as varied as genetics and weather forecasting, because inverse PDEs help scientists work backward from observable patterns to infer the hidden dynamics that produced them.

“Solving an inverse problem is like looking at ripples in a pond and working backward to figure out where the pebble fell,” says Vivek Shenoy, Eduardo D. Glandt President’s Distinguished Professor in Materials Science and Engineering (MSE) and senior author of a study published in Transactions on Machine Learning Research (TMLR), which will be presented at the Conference on Neural Information Processing Systems (NeurIPS 2026). “You can see the effects clearly, but the real challenge is inferring the hidden cause.”

A new way to understand the evolution of spacetime dynamics

The concept of spacetime, first described in Einstein’s theory of general relativity, has since been widely studied by many physicists worldwide. Spacetime is described mathematically as a four-dimensional (4D) continuum in which physical events occur, which merges three-dimensional (3D) space, with one-dimensional (1D) time.

This 4D continuum is known to continuously evolve following complex and intricate patterns that are governed by Einstein’s field equations; mathematical equations that describe how matter and energy shape spacetime. While various past theoretical studies explored the evolution of spacetime, identifying patterns that persist during its evolution has proved challenging so far.

Researchers at Adolfo Ibáñez University in Chile and Columbia University set out to explore the evolution of spacetime using ideas rooted in nonlinear electrodynamics, an area of physics that studies the behavior of electric and magnetic fields in complex materials.

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