Reasons Revealed for the Brain’s Elastic Sense of Time

Our sense of time may be the scaffolding for all of our experience and behavior, but it is an unsteady and subjective one, expanding and contracting like an accordion. Emotions, music, events in our surroundings and shifts in our attention all have the power to speed time up for us or slow it down. When presented with images on a screen, we perceive...

22h

Physicists Argue That Black Holes From the Big Bang Could Be the Dark Matter

Black holes are like sharks. Elegant, simple, scarier in the popular imagination than they deserve, and possibly lurking in deep, dark places all around us. Their very blackness makes it hard to estimate how many black holes inhabit the cosmos and how big they are. So it was a genuine surprise when the first gravitational waves thrummed through detectors...

1d

The Simple Math Problem We Still Can’t Solve

This column comes with a warning: Do not try to solve this math problem. You will be tempted. This problem is simply stated, easily understood, and all too inviting. Just pick a number, any number: If the number is even, cut it in half; if it’s odd, triple it and add 1. Take that new number and repeat the process, again and again. If you keep this...

2d

At the International Mathematical Olympiad, Artificial Intelligence Prepares to Go for the Gold

The 61st International Mathematical Olympiad, or IMO, begins today. It may go down in history for at least two reasons: Due to the COVID-19 pandemic it’s the first time the event has been held remotely, and it may also be the last time that artificial intelligence doesn’t compete. Indeed, researchers view the IMO as the ideal proving ground for machines...

3d

How Mathematical ‘Hocus-Pocus’ Saved Particle Physics

In the 1940s, trailblazing physicists stumbled upon the next layer of reality. Particles were out, and fields — expansive, undulating entities that fill space like an ocean — were in. One ripple in a field would be an electron, another a photon, and interactions between them seemed to explain all electromagnetic events. There was just one problem:...

1w

A New Algorithm for Graph Crossings, Hiding in Plain Sight

This past October, as Jacob Holm and Eva Rotenberg were thumbing through a paper they’d posted a few months earlier, they realized they had been sitting on something big. For decades computer scientists had been trying to develop a fast algorithm for determining when it’s possible to add edges to a graph so that it remains “planar,” meaning none of...

2w

‘Trained Immunity’ Offers Hope in Fight Against Coronavirus

Laboratories around the world are in a high-profile race to create vaccines that might help end the COVID-19 pandemic. More quietly, however, other scientists are investigating whether a vaccine that has already been in use for decades could also confer some level of protection. Recent analyses of global epidemiological data by several teams in the...

2w

When Math Gets Impossibly Hard

We like to say that anything is possible. In Norton Juster’s novel The Phantom Tollbooth, the king refuses to tell Milo that his quest is impossible because “so many things are possible just as long as you don’t know they’re impossible.” In reality, however, some things are impossible, and we can use mathematics to prove it. People use the term “impossible”...

2w

Mathematicians Open a New Front on an Ancient Number Problem

As a high school student in the mid-1990s, Pace Nielsen encountered a mathematical question that he’s still struggling with to this day. But he doesn’t feel bad: The problem that captivated him, called the odd perfect number conjecture, has been around for more than 2,000 years, making it one of the oldest unsolved problems in mathematics. Part of...

2w

How Two Became One: Origins of a Mysterious Symbiosis Found

Symbiotic relationships between bacteria and multicellular organisms are everywhere in nature, but some are more intricately intertwined than others. Both cows and carpenter ants, for example, rely on bacterial partners in their digestive systems to help them get the most out of their food. Yet while the cows’ bacteria merely inhabit the animals’ stomach,...

3w