Latest news with #Anaxagoras
Scientific American
a day ago
- Science
- Scientific American
Math Breakthroughs from Behind Bars
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 difficult in ways that she didn't anticipate. She couldn't summon the energy to delve into Levine's work applying algebraic topology to algebraic varieties (which is just as challenging as it sounds). Instead she distracted herself with daydreams about doing 'beautiful math,' as she described it in an online essay, and completing her doctoral thesis under Levine's supervision. She later pursued graduate studies with Levine, earned her Ph.D. and, after defending her thesis, shared her extraordinary backstory with her colleagues. On supporting science journalism If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today. Yakerson is not alone. Several renowned mathematicians gained invaluable experience despite the challenges of incarceration. As the ancient Greek philosopher and historian Plutarch noted while describing the accomplishments of the scholar Anaxagoras, 'There is no place that can take away the happiness of man, nor yet his virtue or wisdom.' Anaxagoras of Clazomenae: Steadfast Heretic In the fifth century B.C.E., Greek philosopher Anaxagoras refused to recognize the sun as a deity. Instead he declared that the moon shines because it reflects the sun's light and that the moon and sun were objects, not gods. These statements were heretical in Athens, where Anaxagoras lived. Exactly what happened next is still somewhat up for debate, but Plutarch records that Anaxagoras was imprisoned. Records suggest he only escaped the death penalty because of his close relationship with Pericles, an important Athenian statesman. To pass the time in prison, Anaxagoras attempted to construct a square with the same area as a circle. He tackled this feat, 'squaring a circle,' with nothing more than a string, an unmarked ruler and a pencil. Ultimately, he failed. Despite his success in theoretical astronomy, this particular task was doomed from the start. More than 2,000 years later, other scholars would determine that it couldn't be any other way. In the 19th century mathematicians discovered that squaring the circle with only a ruler and compass is impossible. This proof was itself made possible by a mathematical theory developed by Évariste Galois, who, incidentally, was also imprisoned in his lifetime, in his case for proposing a toast to the death of the French king. Tibor Radó: Escape into Infinity Hungarian-born Tibor Radó began studying engineering in the early 20th century but was forced to abandon his studies shortly after the outbreak of World War I. He served as a soldier on the Russian front and ended up in a Siberian prisoner of war camp in 1916. There he met Austrian mathematician Eduard Helly, who was also imprisoned. In the years that followed, Helly introduced the inquisitive Radó to the fundamentals of mathematical research. During the riots caused by Russia's White Army in 1919, Radó managed to escape from the prison camp and fight his way through Siberia on foot. The young man traveled more than 1,000 kilometers to his homeland of Hungary, which he finally reached in 1920. There he resumed his studies—this time, however, he chose mathematics, inspired by Helly, with whom he maintained close contact until Helly's death in 1943. Throughout his career, Radó explored the limits of mathematics. He succeeded in constructing numbers and functions that are 'uncomputable,' or beyond the reach of even the most powerful supercomputers. André Weil: Pacifist Border Crosser As geopolitical tensions increased worldwide in the 1930s, mathematician André Weil, a committed pacifist, sought to avoid French military service and emigrated to the U.S. Weil was on a research trip to Finland when World War II broke out in 1939. Shortly thereafter, he was arrested on suspicion of espionage after Finnish authorities found suspicious writings in his possession. 'The manuscripts they found appeared suspicious—like those of Sophus Lie, arrested on charges of spying in Paris, in 1870,' Weil later recalled. The authorities also uncovered rolls of paper, which Weil reported as the text of a novel by Honoré de Balzac, a letter in Russian and calling cards that displayed a pseudonymous name used by Weil and other French mathematicians. Fortunately, renowned Finnish mathematician Rolf Nevanlinna was able to convince the authorities to deport Weil to Sweden. From there, he was extradited via the U.K. to France, where he was imprisoned again for evading military service. While imprisoned in Rouen, France, Weil developed one of the most ambitious programs in mathematics, which experts are still working on today: a kind of Rosetta stone connecting seemingly disparate fields (number theory, algebra and geometry). Mathematics in Prison Today These four are just a few of many examples of imprisoned people who made important discoveries for the field or encountered mathematical concepts that would set their careers on bold new trajectories. A particularly compelling case is that of Christopher Havens, an incarcerated person who was convicted of murder in 2010. Havens founded the Prison Mathematics Project, or PMP, to make mathematical research accessible to people in prison in the U.S. As Havens discovered, accessing specialized content in prison is extremely difficult. Prison libraries are generally poorly equipped, and incarcerated people generally lack Internet access. PMP addresses that need, in part through a mentoring program by which interested people in prison can exchange ideas with mathematicians. It's been a successful project in many ways. Some incarcerated people have published their first professional publications through it. And given the long history of mathematical breakthroughs begun behind bars, I'm excited to see what mathematical breakthroughs it will produce in the future.
Yahoo
18-07-2025
- Science
- Yahoo
Scientists Just Solved a Solar Mystery That Baffled Humanity For Centuries
Here's what you'll learn when you read this story: Why sunspots are able to last so long has been a mystery for millenia, but a new observation technique revealed their secret. The equilibrium between magnetic fields and pressure allows the solar blotches to remain stable anywhere from days to months. Despite being darker, cooler regions of the sun, sunspots are related to its hot temper, and can help predict solar outbursts like flares and coronal mass ejections. Sunspots were observed on the surface of our star centuries before Galileo suffered eye damage peering at them through his telescope. The first known records were written down by Chinese astronomers in 27 B.C., but observation may go even further back if Greek philosopher Anaxagoras really, ahem, spotted one in 467 B.C. While some of the ancients thought that these shadows on our star meant changes in the cosmos, sunspots are surprisingly stable—and now we know why. Sunspots are actually byproducts of magnetic field chaos. Inside the sun's convective zone, scorching plasma cools as it moves towards the solar surface, taking energy with it. This plasma becomes denser as it loses heat and sinks, forming cooler dark spots until heat from further inside the sun causes it to rise again. And all the while, magnetic fields keep twisting and breaking and rearranging themselves. This explains the association of sunspots with the outbursts we know as solar flares and coronal mass ejections, which can release enough electromagnetic radiation to threaten satellites and electrical infrastructure on Earth. More stable sunspots can possibly give more insight to the solar activity cycle, which is about 11 years long and peaks during a solar maximum. Previous explanations for their stability suggested an equilibrium between magnetic fields and gas pressure, but magnetic turmoil has long made this difficult to observe. Now, an international research team using Germany's GREGOR solar telescope has finally cleared up the hazy observations of sunspots with a new method that removes interference from Earth's atmosphere and reveals strikingly clear images. Led by researchers from the Institute of Solar Physics in Freiburg, Germany, the technique—originally developed at the Göttingen Max Planck Institute for Solar System Research—has achieved what only (much more expensive) satellites were able to do before: it made the analysis of polarized light from the Sun possible. Polarization is the phenomenon of light's electric field moving back and forth, perpendicular to the direction in which the light wave itself is headed, and light is said to be polarized when it continues to propagate one way (as opposed to scattering). By taking a closer look at polarized light, the team was able to tell exactly where it was coming from within sunspots, and what was going on inside. It turned out that the equilibrium in sunspots is a balance of pressure and magnetism. Magnetic fields are strongest when electrons remain unattached, but as more pressure is exerted, it forces them into pairs and weakens the magnetic field. Just enough pressure balances out the strength of magnetic fields and keeps the sunspots intact for extended periods. This is known as magnetohydrostatic equilibrium, which describes the properties of a gas or fluid (such as solar plasma) in a magnetic field. Because solar plasma can conduct electricity, it supports the magnetic field it interacts with. '[Our] results provide decisive observational and theoretical support for the idea that sunspots slowly evolve around an equilibrium state and are [in] magnetohydrostatic equilibrium, thereby helping to explain their long lifespans,' the researchers said in a study recently published in Astronomy & Astrophysics. Understanding why sunspots—and the solar turbulence that comes with them—can hang around for so long will help us better forecast space weather and possibly prevent blackouts, damage to satellites, and threats to astronauts' health. You Might Also Like The Do's and Don'ts of Using Painter's Tape The Best Portable BBQ Grills for Cooking Anywhere Can a Smart Watch Prolong Your Life? Solve the daily Crossword
