René Descartes is famous for Cogito, ergo sum and his revolutionary approach to philosophy and mathematics. But he also left behind a mysterious 16-page manuscript written in code.

In this episode, we uncover the story of Descartes' hidden notebook, the waterlogged manuscripts that nearly disappeared, and Gottfried Wilhelm Leibniz's dramatic attempt to decipher the coded pages.

At the center of the mystery is a mathematical relationship involving the vertices, edges, and faces of three-dimensional shapes. Today expressed as V − E + F = 2, this relationship became associated with Leonhard Euler and is closely connected to the development of topology.

We'll explore why this mathematics mattered in the seventeenth century, why Descartes may have feared revealing his ideas, and how the mathematics of shapes and connectivity eventually became relevant to our modern digital world.

3 Things You'll Learn

1. Why Descartes wrote in code The story behind Cogitata Privata, Descartes' "I proceed masked" philosophy, and the secret manuscript that disappeared after Leibniz examined it.

2. How V − E + F = 2 works Using cubes and pyramids, we'll see how vertices, edges, and faces combine to produce a remarkably consistent mathematical relationship.

3. Why this old mathematics still matters The episode connects the history of polyhedra to topology and modern applications such as 3D computer graphics and digital modeling.

Sources

Amir D. Aczel, Descartes's Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe

David S. Richeson, Euler's Gem: The Polyhedron Formula and the Birth of Topology

Peter J. Federico, Descartes on Polyhedra: A Study of the "De solidorum elementis"

Matthew L. Jones, The Good Life in the Scientific Revolution

Frances A. Yates, The Rosicrucian Enlightenment

Johannes Kepler, The Harmony of the World

René Descartes, Discourse on the Method

Full source list appears in the episode transcript at https://www.MathScienceHistory.com

📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

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Music: All music is public domain and has no Copyright and no rights reserved. Selections from The Little Prince by Lloyd Rodgers

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Scientists have officially identified a new wild cat species in Bolivia and a new snake species from New Guinea—and one of them is named after Guns N' Roses guitarist Slash. But these discoveries are about much more than a cute cat and a rock-star snake.

In this episode of How Did We Get Here? Science News Tuesday, we look at how scientists identify new species, why some animals can remain hidden in plain sight for centuries, and how modern genetics and genomics are changing our understanding of the tree of life.

From Carl Linnaeus and the origins of scientific classification to DNA analysis and museum specimens, we explore how scientists went from naming what they could see to uncovering evolutionary relationships that aren't visible to the naked eye.

And there's a bigger question: How many species are still out there waiting to be recognized—and could some disappear before we even know they exist?

Three Things You'll Learn

1. How a "new" species can hide in plain sight.

2. Why a snake was named after Slash, and how Slash rocks out for animals!

3. How DNA changed the way we classify life

4. Why discovering species matters for conservation

Welcome to the jungle: newly-discovered snake named after Slash from Guns N' Roses - Field Museum

https://www.scientificamerican.com/article/see-the-first-new-species-of-cat-discovered-in-more-than-a-century-its-adorable

🔗 Explore more on our website: mathsciencehistory.com 📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

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Music: All music is public domain and has no Copyright and no rights reserved. Selections from The Black Book by Lloyd Rodgers

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GH Hardy was a character. He had qualities that were odd, yet endearing. He was a rigorous mathematician. Yet, when he received a letter from Srinivasa Ramanujan, he changed. He learned a new way of equating mathematics, and developed a deep and loving respect for an individual who was never formally educated in math.

This is the story of a man who had the ability to see genius in another person, even when that person couldn't see it in themselves.

🔗 Explore more on our website: mathsciencehistory.com 📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

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Music: All music is public domain and has no Copyright and no rights reserved. Selections from The Little Prince by Lloyd Rodgers

Wondrous Waters from Pixabay

Nature Documentary by James Carter from Pixabay

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In this episode of Math, Science, History, host Gabrielle Birchak does a repost about Subrahmanyan Chandrasekhar, a 19-year-old prodigy whose curiosity during a two-week sea voyage in 1930 led to a groundbreaking discovery. While sailing from India to England, Chandrasekhar, armed only with a notebook and the vast expanse of the ocean, began questioning the fate of stars after they exhausted their fuel.

Explore more on our website: mathsciencehistory.com To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

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Music: All music is public domain and has no Copyright and no rights reserved. On Matters of Consequence from The Little Prince by Lloyd Rodgers

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What happens when women gather?

Throughout the eighteenth century, women across Europe began creating intellectual communities where they could discuss science, mathematics, philosophy, politics, literature, and medicine. During the Enlightenment, these gatherings helped women challenge the idea that intellectual discovery belonged exclusively to men.

Women such as Laura Bassi, Maria Gaetana Agnesi, Émilie du Châtelet, Catharine Macaulay, Caroline Herschel, and many others built on one another's work and created a path for future generations of women in science.

And that path matters far beyond science. When women gather, exchange knowledge, encourage one another, and make room for the next woman, they can change science, politics, education, and society.

Resources

• Read the original "When Women Gather" article • Download my list of eighteenth-century women in science • Laura Bassi, University of Bologna • Émilie du Châtelet's translation of Newton's Principia, Bibliothèque nationale de France • A Vindication of the Rights of Woman, Library of Congress • Caroline Herschel, Royal Astronomical Society

🔗 Explore more on our website: mathsciencehistory.com 📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

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Music: All music is public domain and has no Copyright and no rights reserved. Selections from The Little Prince by Lloyd Rodgers

Until 2027, carpe diem!

Your job is what you do, not who you are - and that distinction could change your life. Gabrielle Birchak spotlights the astonishing story of Paul Tannery, a daytime engineer in the French tobacco administration whose after-hours curiosity helped reshape the history of mathematics and science.If you've ever felt like your work has started to define your entire identity, this episode offers a powerful reset. Gabrielle makes the case for building a second life around curiosity, hobby, and learning - not as a luxury, but as a source of well-being, purpose, and even legacy.You'll discover:

· Why meaningful interests outside work are linked to lower stress and higher life satisfaction

· How hobbies and non-work activities can strengthen mental health across cultures

· Why curiosity matters even when it never becomes "productive"

· The surprising power of sharing what you learn with other people

· A simple 20-minute weekly practice to become more than your job title

Gabrielle connects Tannery's life to modern research, including findings on psychological detachment from work and global studies on hobby engagement and mental well-being. The result is a short episode with a big message: the things you pursue for joy may end up shaping your life more than the work that pays the bills. Perfect for anyone feeling stuck in their role, hungry for a fuller identity, or looking for permission to follow their curiosity again. If you need a reminder that learning for its own sake still matters, this one will leave you thinking differently about your time, your talents, and your future.

· "Your job is what you do, but it does not have to be who you are."

· "Curiosity is not a distraction from life. It is one of the things that makes life richer."

· "Knowledge grows when it is shared."

🔗 Explore more on our website: mathsciencehistory.com 📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

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Music: All music is public domain and has no Copyright and no rights reserved. Selection is from The Little Prince by Lloyd Rodgers Subscribe on your favorite podcast platform

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Paul Tannery didn't begin his career intending to become one of the most influential historians of mathematics. He trained as an engineer at the École Polytechnique and spent much of his professional life working in France's state tobacco administration. But after work, Tannery pursued a very different passion: ancient mathematics, astronomy, philosophy, and the history of science.

What began as an intellectual interest became a lifetime of scholarship.

1. How Paul Tannery transformed a personal passion into groundbreaking scholarship 2. Why Tannery believed historical claims needed evidence, not repetition 3. Why your "side interest" may matter more than you realize

RESOURCES:

Paul Tannery — MacTutor History of Mathematics Archive

René Taton, "Paul Tannery (1843–1904) Palatine Library - Complesso Monumentale della Pilotta

🔗 Explore more on our website: mathsciencehistory.com 📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

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Music: All music is public domain and has no Copyright and no rights reserved. Selections from The Little Prince by Lloyd Rodgers

Waiting for You by Pawel Feszczuk – from Free Music Archive – CC 4.0

Train by Sergey Cheremisinov -from Free Music Archive – CC 4.0

Serene Sonnet by Oleskii Holubiev from Pixabay – CC 0.0

Until next time, carpe diem!

In this episode of Momentum Monday, I cover how the ancient mathematician Diophantus, who revolutionized problem-solving by focusing on relationships between numbers, can inspire us to rethink our own relationships. Instead of fixating on fixing others, I challenge you to observe, question, and experiment with your connections, just like solving an equation. Whether it's a coworker, family member, or friend, I share how curiosity, pattern recognition, and small changes can shift the momentum in your favor. Plus, I reference research from Albert Bandura, Daniel Kahneman, and B.F. Skinner to ground these ideas in psychology.

🔗 Sources & Further Reading:

• Diophantus and the Birth of Algebra
• Albert Bandura's Social Learning Theory
• Daniel Kahneman's Thinking, Fast and Slow
• B.F. Skinner Science and Human Behavior

3 Things You'll Learn

1. How to observe relationships like a mathematician, identify patterns, not just problems.
2. Why questioning your assumptions (e.g., "Are they ignoring me or overwhelmed?") prevents misunderstandings.
3. How to experiment with small changes to shift the dynamic in any relationship.

🔗 Explore more on our website: mathsciencehistory.com 📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co/d/g3OuP9h

🎧 Enjoying the Podcast? 🔗 Explore more on our website: mathsciencehistory.com

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Music: All music is Public Domain Mark 1.0 Universal and has no Copyright and no rights reserved. Selections from Violin Machine: A Deconstruction of the Bach Concerto by Lloyd Rodgers Until next time, carpe diem!

AI may verify proofs, but it can't replace curiosity. In this episode, I travel back nearly 1,800 years to meet Diophantus of Alexandria and explore how his approach to mathematics still shapes modern problem-solving, from Fermat's Last Theorem to today's AI-assisted research. Along the way, we discover why the real value of mathematics isn't finding answers. it's learning how to think.

🌐 Website: https://www.MathScienceHistory.com

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• Discover why Diophantus is considered one of history's most influential mathematicians. • Learn how his work inspired Fermat's Last Theorem centuries later. • Explore whether AI is changing mathematics. or simply giving mathematicians better tools.

Follow the show, subscribe wherever you listen, and leave a review to help others discover Math! Science! History!

Music: All music is public domain and has no Copyright and no rights reserved. Selections from The Little Prince by Lloyd Rodgers Valorium – by It's Trigi – No Copyright and no rights reserved Documentary Background – by MiroMax Music – No Copyright and no rights reserved Blackbook 7/1/01 from On The Sensations of Tone – by Lloyd Rodgers – No Copyright and no rights reserved Galliard á3 in g by Orlando Gibbons - recorded, mixed, and mastered by Dr. Phillip W. Serna - licensed under the Creative Commons Attribution-Share Alike 4.0 International license Cute loop [c major] [93bpm] by deadrobotmusic -- https://freesound.org/s/555708/ -- License: Creative Commons 0

Subscribe on your favorite podcast platform Leave a review! It helps more people discover the show! Share this episode with friends & fellow history buffs! Until next time, carpe diem! - Gabrielle

Can mathematics be patented? In this episode, I explore one of the most fascinating questions in mathematics, intellectual property, and computer science by tracing the history of patents from the ancient world to today's software and AI algorithms. Along the way, we'll discover why mathematical ideas themselves remain unpatentable while the innovative ways we apply them can change technology, and the future.

🌐 Website: https://www.MathScienceHistory.com ☕Support the show: https://paypal.com/ncp/payment/PR7F7ST49GDNA

You'll learn:

• Why mathematics itself cannot be patented but mathematical applications sometimes can. • How ancient patent and copyright ideas evolved into modern intellectual property law. • How the MP3, Fourier Series, FFT, and the Alice v. CLS Bank case shaped today's software patents.

Follow the show, subscribe on your favorite podcast platform, and leave a review to help more people discover Math! Science! History! Music: All music is public domain and has no Copyright and no rights reserved. Selections from The Little Prince by Lloyd Rodgers

Subscribe on your favorite podcast platform! Leave a review! It helps more people discover the show! Share this episode with friends & fellow history buffs!

Until next time, carpe diem!