A New Quantum Math of Cryptography

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

Astronomers are ready to search for the fingerprints of life in faraway planetary atmospheres. But first, they need to know where to look — and that means figuring out which planets are likely to have atmospheres in the first place.The story How Undergraduate The Road Map to Alien Life Passes Through the ‘Cosmic Shoreline’ first appeared on Quanta Magazine.

We’re living in the golden age of cryptography. Since the 1970s, we've had more confidence in encryption than ever before. But there's a difference between confidence and absolute certainty. And computer scientists care a lot about that difference.The search is always on for better, more secure secrets. But is it possible for digital security to be truly, provably unbreakable? Maybe, with a little help from math and physics. On this week’s episode, host Samir Patel talks with 𝘘𝘶𝘢𝘯𝘵𝘢 computer science staff writer Ben Brubaker about a developing frontier of digital security: quantum cryptography. 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 from the Bletchley Park Trust.

How many oranges can you fit in a box? Mathematicians are obsessed with perfecting their answer to this question in not just our familiar three-dimensional world, but in higher and higher dimensions beyond it. For several decades, they've made only minimal progress toward finding an optimal solution. Then, this past April, an outsider to the field named Boaz Klartag posted a proof that bested these previous records by a significant margin.In this episode of The Quanta Podcast, host Samir Patel and Quanta math staff writer Joseph Howlett discuss how Klartag resuscitated an old technique that experts had abandoned decades earlier to optimize sphere packing in any arbitrarily high dimension. 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 created by Daniel Simion

A young computer scientist and two colleagues show that searches within data structures called hash tables can be much faster than previously deemed possible.The story How Undergraduate Upends a 40-Year-Old Data Science Conjecture first appeared on Quanta Magazine.

As far as we know, quantum mechanics is a universal theory that explains matter and light more or less perfectly. It shows us why atoms don't collapse and why electrons don't spiral into the nucleus of the atom. It explains why glass is clear, why grass is green, why the sky is blue. But no one fully understands how the math of quantum mechanics connects with the reality we live in. One could spend a lifetime getting into the weeds and still have unanswered questions. In honor of quantum mechanics’ 100th birthday, host Samir Patel talks with Quanta physics staff writer Charlie Wood about his recent journey to the birthplace of quantum mechanics, a German island in the North Sea. On Helgoland, Charlie asked physicists many questions about many worlds over many beers. 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.

When some people smell the molecule benzyl acetate, they identify a distinctly banana-y scent. But when others sniff the same compound, they get hints of nail polish remover. How can this be? Smell is a tricky sensory process to pin down. Our perception of scents is wide-ranging and often depends on lived experience. But researchers are building a deeper understanding of the processes underlying our noses’ elusive machinery. In this episode, host Samir Patel and 𝘘𝘶𝘢𝘯𝘵𝘢 biology staff writer Yasemin Saplakoglu explore the invisible sense that shapes our reality, from nostalgic childhood fragrances — lavender, old books — to familiar irksome odors — skunks, garbage. 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.

By screening films in a brain scanner, neuroscientists discovered a rich library of neural scripts — from a trip through an airport to a marriage proposal — that form scaffolds for memories of our experiences.The story How ‘Event Scripts’ Structure Our Personal Memories first appeared on Quanta Magazine.