CuriousMinds

Math Breakthroughs from Behind Bars

People in prisons and jails have contributed to some of the greatest ideas in mathematics

In 2014 Mura Yakerson, a college student at the time, decided to practice driving in a quiet area in the countryside near Saint Petersburg, Russia. Then something went wrong. While she was pulling out of a parking space, Yakerson accidentally damaged another car. This incident turned out to be the beginning of a nightmare.

Because she drove away from the scene, unaware that she had hit another vehicle, a judge later charged Yakerson with leaving the place of an accident and then gave her the choice between a one-year driving ban or three days in jail. Yakerson chose incarceration. She thought that, away from distractions, she could devote herself to understanding a challenging paper by mathematician Marc Levine of the University of Duisburg-Essen in Germany.

But those three days were…

Organisms can produce energy from air

The findings point to new possibilities for sustainable energy production

Researchers from the University of Bern, in collaboration with researchers from Australia and New Zealand, have recreated an important process in the laboratory that enables organisms to obtain Energy directly from components found in air. This confirms that certain organisms such as bacteria can actually live on air alone, without relying on sunlight or other energy sources. The findings point to new possibilities for sustainable energy production.

Hydrogen occurs in our atmosphere only as a trace gas, in a concentration of 0.00005%. The concentration remains almost constant, despite 70 million tons of newly produced hydrogen every year – mainly through photochemical processes and human-induced production. The reason for this constancy was unclear for a long time, but it is now known that most of it is absorbed by microorganisms such as bacteria in the…

Famous double-slit experiment holds up when stripped to its quantum essentials

MIT physicists have performed an idealized version of one of the most famous experiments in quantum physics. Their findings demonstrate, with atomic-level precision, the dual yet evasive nature of light. They also happen to confirm that Albert Einstein was wrong about this particular quantum scenario.

The experiment in question is the double-slit experiment, which was first performed in 1801 by the British scholar Thomas Young to show how light behaves as a wave. Today, with the formulation of quantum mechanics, the double-slit experiment is now known for its surprisingly simple demonstration of a head-scratching reality: that light exists as both a particle and a wave.

Stranger still, this duality cannot be simultaneously observed. Seeing light in the form of particles instantly obscures its wave-like nature, and vice versa.

The original experiment involved shining a beam of light through two…

Scientists discover the moment AI truly understands language

A study in JSTAT describes the sharp shift in text comprehension strategies during neural network training.

The language capabilities of today's artificial intelligence systems are astonishing. We can now engage in natural conversations with systems like ChatGPT, Gemini, and many others, with a fluency nearly comparable to that of a human being. Yet we still know very little about the internal processes in these networks that lead to such remarkable results.

A new study published in the Journal of Statistical Mechanics: Theory and Experiment (JSTAT) reveals a piece of this mystery. It shows that when small amounts of data are used for training, neural networks initially rely on the position of words in a sentence. However, as the system is exposed to enough data, it transitions to a new strategy based on the meaning of the words. The study finds that this…