When pigeons outnumber pigeonholes, some birds must double up. This obvious statement — and its inverse — have deep connections to many areas of math and computer science. The story How a Problem About Pigeons Powers Complexity Theory first appeared on Quanta Magazine.

Every summer since 1983, scientists at Crater Lake National Park have gathered data about the lake’s famous clarity. This past summer, Quanta contributing writer Rachel Nuwer journeyed with them as they conducted their annual tests. On this week’s episode, Nuwer and host Samir Patel discuss what gives the lake its vivid blue color, and what its data can tell us about the way water moves through a deep temperate lake. Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda recorded at Crater Lake National Park in July 2010 by the National Park Service Natural Sounds Program.

How do sellers decide how to price their goods? Competition should keep prices down, while collusion can rig higher prices (and break the law). On this week’s episode, host Samir Patel speaks with staff writer Ben Brubaker about how computer scientists are using game theory to see how algorithms might result in high prices without shady backroom deals. This topic was covered in a recent story for Quanta Magazine.   Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Tom 7's YouTube channel Audio coda from FDR Presidential Library & Museum.

At first glance, studying the math of waves seems like it should be smooth sailing. But the equations that describe even the gentlest rolling waves are a mathematical nightmare to solve. On this week’s episode, host Samir Patel speaks with math staff writer Joseph Howlett why waves are so elusive, even in a simplified world of equations. This topic was covered in a recent story for Quanta Magazine.   Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda is "The Merry Golden Tree" by Shovel Dance Collective.

Salvador Dalí, Thomas Edison and Edgar Allan Poe all took inspiration from the state between sleep and waking life. On this week’s episode, host Samir Patel speaks with biology staff writer Yasemin Saplakoglu about how brain systems dictate the strange transitions into and out of sleep. This topic was covered in a recent story for Quanta Magazine.   Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda: Copyright in The Mike Wallace Interview with Salvador Dalí is owned by the University of Michigan Board of Regents and managed by Bentley Historical Library, University of Michigan. The Harry Ransom Center (HRC) at the University of Texas, Austin University Libraries, is the owner of the physical kinescope.

A powerful mathematical technique is used to model melting ice and other phenomena. But it has long been imperiled by certain “nightmare scenarios.” A new proof has removed that obstacle. The story A New Proof Smooths Out the Math of Melting first appeared on Quanta Magazine.

Recently, astrophysicists identified something peculiar: An enormous “naked” black hole with no galaxy in sight. On this week’s episode, host Samir Patel speaks with physics staff writer Charlie Wood about how the strange little red dot is upending our assumptions of the first billion years of cosmic history. This topic was covered in a recent story for Quanta Magazine.   Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda courtesy of Caltech/MIT/LIGO Lab.

Thanks to a delicate interplay between plate tectonics and life, Earth’s thermostat has kept animal life thriving on our planet for half a billion years. On this week’s episode, host Samir Patel speaks with contributing writer Peter Brannen about our planetary highs and lows, and the precarious goldilocks zone our animal-filled finds itself in now. This topic was covered in a recent story for Quanta Magazine.   Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda courtesy of Martin Rietze's YouTube channel.

A new proposal makes the case that paraparticles — a new category of quantum particle — could be created in exotic materials. The story ‘Paraparticles’ Would Be a Third Kingdom of Quantum Particle first appeared on Quanta Magazine.

Imagine a set of simple building blocks that can self-assemble into any shape you want. The possibilities for such a technology could be boundless. Inspired by nature, “complexity engineering” seeks to design such blocks, building on a classic computer simulation. On this week’s episode, host Samir Patel speaks with contributing writer George Musser about recent developments in so-called cellular automata. This topic was covered in a recent story for Quanta Magazine.   Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda courtesy of the Simons Foundation. 

Around 6,000 years ago, the Sahara was a lush grassland. Then, as if a switch flipped, it began to dry out, becoming the desert that we know today. Tipping points are moments in Earth’s history where gradual change suddenly becomes rapid and forms a new equilibrium. They’re one of the most alarming threats of our planet’s near future — and one of the most uncertain. When will a tipping point occur? Mathematicians are attempting to turn vague, apocalyptic visions into something that we can actually prepare for and deal with. On this week’s episode, host Samir Patel speaks with contributing writer Gregory Barber about what tipping points can — and cannot — tell us about the future of our planet. This topic was covered in a recent story for Quanta Magazine. Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda courtesy of Gresham College. 

It’s been difficult to find important questions that quantum computers can answer faster than classical machines, but a new algorithm appears to do it for some critical optimization tasks. The story Quantum Speedup Found for Huge Class of Hard Problems first appeared on Quanta Magazine.

“Memory” means many things to many people, and in many fields. We tend to understand memory to be a phenomenon that happens primarily in the brain, but in recent years, researchers have understood memory as a physical phenomenon that can occur in plenty of systems. On this episode, contributing writer Claire L. Evans tells host Samir Patel about how neuroscientists are probing the memory of individual cells. Audio coda courtesy of YACHT.

The climate is changing. So is the way we understand the climate. On this week's episode, contributing writer Zack Savitsky joins host Samir Patel to discuss his recent reporting on the rich history and uncertain future of climate modeling, the field of science that blends math, physics, and earth science to predict the behavior of our planet's complex climate system. Audio coda courtesy of Princeton University

Rare and powerful compounds, known as keystone molecules, can build a web of invisible interactions among species. The story A New, Chemical View of Ecosystems first appeared on Quanta Magazine.

In order to trust machines with important jobs, we need a high level of confidence that they share our values and goals. Recent work shows that this “alignment” can be brittle, superficial, even unstable. In one study, a few training adjustments led a popular chatbot to recommend murder. On this episode, contributing writer Stephen Ornes tells host Samir Patel about what this research reveals. Audio coda from The National Archives and Records Administration.

For most of us, the word “climate” immediately generates thoughts of melting ice, rising seas, wildfires and gathering storms. However, in the course of working to understand this pressing challenge, scientists have revealed so much more: A fundamental understanding of how Earth’s climate works.  Quanta recently published a nine-story series that investigates this basic science. On this episode of The Quanta Podcast, senior editor Hannah Waters joins editor in chief Samir Patel to discuss how humans have come to understand our planet. Crying Glacier Audio Coda by Ludwig Berger, Lutz Stautner and Philipp Becker

The deceptively simple Kakeya conjecture has bedeviled mathematicians for 50 years. A new proof of the conjecture in three dimensions illuminates a whole crop of related problems. The story ‘Once in a Century’ Proof Settles Math’s Kakeya Conjecture first appeared on Quanta Magazine.

In the field of harmonic analysis, there’s a constellation of questions about how the energy of a wave concentrates. Earlier this year, a 17-year-old high school student named Hannah Cairo solved a 40-year-old mystery about how some of these waves behave, surprising and exciting mathematicians. Cairo has not yet obtained a high school or undergraduate degree, but she recently began a doctoral program at the University of Maryland to continue her already impressive career studying mathematics. In this week's episode, math editor Jordana Cepelewicz joins host Samir Patel to discuss the significance of Cairo's proof. Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.

In science textbooks, Earth looks like a round layer cake. There's a hard line between the liquid metal core and the putty-like rock mantle. But maybe that boundary is a little fuzzier than we previously thought. Strange, continent sized blobs rest on the dividing line. These blobs are leaching material from the Earth’s core, extending arms out into the mantle, and sending core material up and out through magmatic plumes.  No one's completely sure how it’s happening. On this week’s episode, host Samir Patel and writer Robin George Andrews dig into the ancient isotopic signatures that are helping us better understand the material bubbling up from the depths of our planet. This topic was covered in a recent story for Quanta Magazine. Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel speaks with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math. Audio coda courtesy of wildlife photographers Gudmann & Gyda