We explore Jeremy Bernstein's manifold-based approach to AI stability: constraining weight matrices to lie on a Stiefel manifold keeps singular values near one, making layers behave like rotations and improving predictability. Extending to modular manifolds, we treat each block as its own manifold with its own norm, and compose them so constraints stack cleanly, enabling automatic learning-rate budgeting across transformers. Along the way we compare to standard tricks like layer norm and grad...

A half-century tale of a metal that was once the pinnacle of opulence and is now everywhere. Aluminum’s abundance in ore didn’t matter—refining it was brutally hard until the Hall–Héroult breakthrough in 1886. Coupled with the rise of cheap electricity, this unlocked mass production and crashed the price, transforming aluminum from precious parlorware into a universal building material. From Napoléon III’s special cutlery to airplanes, engines, and soda cans, the episode traces how utility an...

Join us as we explore A000360, the OEIS entry counting non-degenerate triangles inside a self-similar fractal rep-4 tile. We’ll break down the geometry of the fractal and what counts as a triangle, then uncover the surprising number-theoretic connections: the distribution ties to the Stern–Brocot sequence (A02487) via a modulo-3 reduction, with dropping the first term yielding AA00360. We’ll also discuss the tidy recurrence governing even-index terms, revealing a hidden arithmetic order behin...

The sources collectively explore the concept of harmony and relationality in contrast to radical individualism, drawing on both Eastern and Scottish philosophies. One source advocates for reclaiming an ancient Gaelic philosophy of "harmonious doing," exemplified by communal land use like the lazybed (feannagan) and the restorative nature of Brehon Laws, arguing this approach offers a path beyond modern alienation. Supporting this idea, another source provides excerpts from a talk by Alan Watt...

Tim Harford investigates some of the numbers in the news. This week:Nigel Farage says 6.5 million people are on out-of-work benefits – with some benefits up 80% since 2018. Are those numbers right?Do French pensioners really earn more than their working-age compatriots?How is it possible for one kilogram of fish food to produce one kilogram of salmon?And do we really have five senses?If you’ve seen a number you think we should take a look at, email the team: moreorless@bbc.co.ukPresenter: Tim

Join us as we untangle the mathematical ‘ghosts’ of quantum field theory—from Faddeev–Popov ghosts that preserve gauge symmetry to Goldstone modes that become W and Z bosons, and the troublesome negative-norm states that threaten unitarity and causality. A clear, accessible tour of why these unphysical states matter for regularization, mass generation, and the foundations of physics. Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical inf...

We dive into the 1859 Carrington storm — the first recorded solar flare and the fastest CME on record — and unravel how it lit up skies worldwide, crashed telegraph systems, and hinted at a sun-driven vulnerability in today’s electrical grid. From the auroral spectacle to near-miss modern-day scenarios, we connect history to present-day risk and explore whether the sun could unleash even bigger storms beyond Carrington’s benchmark. Note: This podcast was AI-generated, and sometimes AI can mak...

This week, Pappus of Alexandria, a pivotal figure in 4th-century mathematics. Often considered one of the last great Greco-Roman geometers, Pappus compiled the monumental Synagogue, a comprehensive collection that sought to revive classical Greek geometry. In this episode: A candid look at Pappus's personality and his notorious public critique of the female mathematician Pandrosion and her student. Pappus’s distinction between "plane," "solid," and the more expansive "linear" problems. Concepts like

In this episode of Ordinarily Extraordinary – Conversations with Women in STEM, Kathy and Linda sit down with Lawanda Parnell, a retired technology and utility leader whose career began at IBM in the early 1980s and spanned decades of innovation and leadership. Lawanda shares her journey from studying business administration with a strong math and computer science foundation at the University of Florida, to becoming one of the few Black women in tech during her era, to leading large-scale pro...

With the news that there’s a new computing education podcast (The Rest is Teaching) I thought I’d put together a selection of podcasts which might be of interest to computing educators. The first set are more specifically about teaching computing, or computing careers but the second set are… a little more random. Perhaps you have […]

Number of the Day - "365" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Join Danny Moore and Aaron Jurgaitis as they discuss tertiary and quaternary care from an actuarial perspective. Danny and Aaron discuss: Definitions around the different levels of care, from primary up to quaternary Specifics around the types of care delivered in the specialized facilities that deliver this care, and The key themes actuaries need to keep in mind when analyzing data that include these types of services. Aaron shares information from his background of performing analysis for

Send us a text Does your math class feel like only a handful of students ever raise their hands while the rest stay silent? Or maybe your students avoid sharing out of fear of being wrong? You’re not alone—many teachers face this challenge. In today’s episode, we’re diving into Step 3 of Word Problem Workshop: the Share, and how it can transform your math classroom into a motivated community of problem-solvers. When I taught both 1st and 5th grade, I noticed the same pattern—students hesitate...

In this episode of Math! Science! History!, Gabrielle uncovers the fascinating story of quasicrystals, once thought impossible, now proven to exist both in the lab and in meteorites from space. Listeners will learn how quasicrystals challenged centuries of crystallography, the math that explains their strange patterns, and the surprising ways they’re used today, from non‑stick coatings to futuristic photonics. Three Things You’ll Learn Why quasicrystals broke the old definition of crystals and

In this long-awaited followup to our popular Math Club Junior episode, Pete and Noah are back with Mrs. Morrison’s class, as chaperones on a field trip to the local zoo. Listen in as our group of Junior Zookeepers meet a whole new cast of zany characters, and once again learn that math is everywhere if you just look around. And just like last time, this story is full of interesting math challenges for listeners in the upper elementary grades to enjoy and solve.   • A slide deck with visuals to go

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We explore Armenia’s colossal Vizhapakar dragonstones—basalt megaliths dating to the Chalcolithic around 4200–4000 BCE. Shaped as fish and cowhide figures, these markers sit at springs and irrigation corridors, revealing a sophisticated, region‑wide ritual system that tied water management to monumental labor. Through new dating and spatial analysis, we see how these 4,000+ year‑old stones encode social organization, sacred geography, and a worldview where water, ritual, and survival were dee...

We dive into A000351, the powers of five, from its tidy recurrence and generating function to the surprising ways it shows up across number theory, combinatorics, and geometry. Along the way we explore connections to Pisot-number phenomena, a divisor-sum–based lens on primality, counting integers with only odd digits, generating-function identities, and even a fractal-counting angle in the Sierpinski pyramid. We also glimpse neat infinite-series quirks: the sum of reciprocals of 5^n equals 5/...

Explore the birth of the capacitor era. In the 1740s, Kleist and Muschenbroek’s shocking experiments showed a glass jar could store energy; Benjamin Franklin identified the dielectric inside and coined the term 'condenser.' Jean-Antoine Nollet popularized the device and the name 'battery,' turning it into public spectacle and laying the groundwork for modern electronics and the enduring questions about electricity’s true nature. Note: This podcast was AI-generated, and sometimes AI can make m...

Polaritons are bosonic quasi-particles formed when photons strongly couple to a material excitation (such as an exciton or a phonon), creating new mixed light–matter normal modes. This strong coupling leads to level repulsion (avoided crossing) that splits the system into upper and lower polariton branches, giving tunable light propagation inside materials. The result is a powerful platform for energy-efficient devices and quantum technologies, with phenomena like room-temperature polariton s...