Just as scientists test hypotheses, mathematicians prove or disprove conjectures. But what makes a proof stronger than a guess? What does evidence look like in the world of mathematics? Hear Melanie Matchett Wood, professor of mathematics at Harvard University, explain how probability helps to guide number theorists toward certainty.

How Do Mathematicians Know Their Proofs Are Correct?

“The Joy of Why” is a Quanta Magazine podcast about curiosity and the pursuit of knowledge. The mathematician and author Steven Strogatz and the cosmologist and author Janna Levin take turns interviewing leading researchers about the great scientific and mathematical questions of our time. New episodes are released every other Wednesday.

Quanta Magazine is a Pulitzer Prize–winning, editorially independent online publication launched and supported by the Simons Foundation to illuminate big ideas in science and math through public service journalism.  Quanta’s reporters and editors focus on developments in mathematics, theoretical physics, theoretical computer science and the basic life sciences, emphasizing timely, accurate, in-depth and well-crafted articles for its broad discerning audience. In 2023, Steven Strogatz received a National Academies Eric and Wendy Schmidt Award for Excellence in Science Communications partly for his work on “The Joy of Why.”

Science

Life Sciences

For decades, the best drug therapies for treating depression, like SSRIs, have been based on the idea that depressed brains don’t have enough of the neurotransmitter serotonin. Yet for almost as long, it’s been clear that simplistic theory is wrong. Recent research into the true causes of depression is finding clues in other neurotransmitters and the realization that the brain is much more adaptable than scientists once imagined. Treatments for depression are being reinvented by drugs like ketamine that can help regrow synapses, which can in turn restore the right brain chemistry and improve whole body health.In this episode, John Krystal, a neuropharmacologist at the Yale School of Medicine, tells Steve Strogatz about the new findings in mental health research that are revolutionizing psychiatric medication.

What Happens in the Brain to Cause Depression?

If superconductors — materials that conduct electricity without any resistance — worked at temperatures and pressures close to what we would consider normal, they would be world-changing. They could dramatically amplify power grids, levitate high-speed trains and enable more affordable medical technologies. For more than a century, physicists have tinkered with different compounds and environmental conditions in pursuit of this elusive property, but while success has sometimes been claimed, the reports were always debunked or withdrawn. What makes this challenge so tricky?

In this episode, Siddharth Shanker Saxena, a condensed-matter physicist at the University of Cambridge, gives co-host Janna Levin the details about why high-temperature superconductors remain so stubbornly out of reach.

Will Better Superconductors Transform the World?

Milk is more than just a food for babies. Breast milk has evolved to deliver thousands of diverse molecules including growth factors, hormones and antibodies, as well as microbes.

Elizabeth Johnson, a molecular nutritionist at Cornell University, studies the effects of infants’ diet on the gut microbiome. These studies could hold clues to hard questions in public health for children and adults alike. In this episode of “The Joy of Why” podcast, co-host Steven Strogatz interviews Johnson about the microbial components that make breast milk one of the most wondrous biofluids found in nature.

You can read the transcript for this episode and see the image of the micrograph Johnson references on our website.

What Does Milk Do for Babies?

Nothing escapes a black hole… or does it? In the 1970s, Stephen Hawking described a subtle process by which black holes can “evaporate,” with some particles evading gravitational oblivion. This phenomenon, now dubbed “Hawking radiation,” seems inherently at odds with general relativity, but it gets weirder still: If particles can escape, do they preserve some information about the matter that was obliterated? Leonard Susskind, a physicist at Stanford University, found himself at odds with Hawking when it came to answering this question. In this episode, co-host Janna Levin speaks with Susskind about the “black hole war” that ensued and the powerful scientific lessons that have radiated from one of the most famous paradoxes in physics.

Can Information Escape a Black Hole?

Birds flock. Locusts swarm. Fish school. In these chaotic assemblies, order somehow emerges. Collective behaviors differ in their details from one species to another, but they largely adhere to principles of collective motion that physicists have worked out over centuries. Now, using technologies that only recently became available, researchers have been able to study these patterns of collective animal behavior more closely than ever before. These new insights are unlocking some of the secret fitness advantages of living as part of a group rather than as an individual. The improved understanding of swarming pests such as locusts could also help to protect global food security.

In this episode, co-host Steven Strogatz interviews the evolutionary ecologist Iain Couzin about  how and why animals exhibit collective behaviors, and the secret advantages that arise from them.

How Do Mathematicians Know Their Proofs Are Correct?

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