Episode Overview

Once dismissed as mathematical absurdities, black holes are now recognized as real, powerful features of our universe—cosmic wells where space, time, and even light collapse. In this episode of Math! Science! History!, we explore the astonishing story of how black holes evolved from a rejected theory to an accepted reality. From Einstein’s reluctance and Oppenheimer’s overlooked models, to John Wheeler’s advocacy and Stephen Hawking’s revolutionary radiation theory, this episode traces the full arc of scientific discovery—and what black holes reveal about our own place in the cosmos.

 

Three Key Take-Aways

Why Karl Schwarzschild’s World War I-era math predicted black holes decades before anyone took them seriously

How John Wheeler changed the game by naming—and championing—the black hole

What modern observations like Cygnus X-1, Hawking radiation, and LIGO’s gravitational wave detection tell us about collapsed stars and spacetime

Resources & References (the books include affiliate links)

Oppenheimer & Snyder (1939): On Continued Gravitational Contraction

David Finkelstein (1958): Past-Future Asymmetry of the Gravitational Field

Kip Thorne’s book: Black Holes and Time Warps: Einstein’s Outrageous Legacy

Marcia Bartusiak’s book: Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled on by Hawking Became Loved

LIGO and gravitational wave discovery (2015)

🔗 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 🎵 Audio: Podcast mixed by David Aviles

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In this Flashcard Friday episode, Gabrielle dives into the surprising history and science of sunblock. From ancient Egypt’s jasmine oils to modern SPF 50 sprays, discover how sunscreen evolved and why it’s one of the best defenses against deadly melanoma. Gabrielle shares the statistics on skin cancer, explains how sunblock works, and gives you simple tips to stay protected. With her favorite motto, “Just say NO to melanoma,” she’ll leave you ready to face the sun smartly.

3 Things Listeners Will Learn:

- The fascinating history of sunblock, from ancient remedies to modern formulations.

- How sunscreen protects the skin and how to use it correctly for maximum safety.

- Eye-opening facts about melanoma risk, survival rates, and prevention through sun protection.

Resource Links

American Cancer Society: Melanoma Skin Cancer Overview

All About Sunscreen: Why You Need It. How it Works for You

Melanoma Treatment (PDQ®)–Patient Version

Visit us! 

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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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Episode Overview

In this special re-release, we revisit the life and mind of Blaise Pascal, a mathematician, physicist, inventor, philosopher, and theologian who left a lasting impact on multiple disciplines. From his early genius in geometry to his pioneering work in probability theory, Pascal was a thinker who never stopped exploring the boundaries between logic and faith. In this episode, Gabrielle Birchak explores how Pascal’s scientific brilliance intersected with his spiritual journey, shedding light on the man who helped shape modern science, mathematics, and religious philosophy.

Whether you're hearing this episode for the first time or giving it a second listen, Pascal's story continues to resonate through the centuries.

3 Things You Will Learn

How Pascal’s early work in conic sections and projective geometry led to “Pascal’s Theorem.”

Why his collaboration with Fermat on probability theory is considered the foundation of modern decision science.

How Pascal reconciled science and religion through his writings, including Pensées and Pascal’s Wager.

Resources & References

Read the blog: Pascal’s Higher Power

Stanford Encyclopedia of Philosophy – Blaise Pascal

Khan Academy – Pascal’s Triangle and Applications

 

🔗 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

 

🌍 Let’s Connect!

Website: mathsciencehistory.com Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social Instagram: https://www.instagram.com/math.science.history

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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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In this Flashcard Fridays episode of Math! Science! History! Gabrielle Birchak takes listeners on a journey aboard the HMS Beagle with a young, seasick Charles Darwin. This wasn’t just a travel story, it was a five-year working holiday that would ultimately change the course of science. Through field observations, curiosity, and a bit of chaos, Darwin unknowingly gathered the seeds of his future theory of evolution.

From the Galápagos Islands to fossil beds in South America, Gabrielle uncovers how a break from academia became one of the most pivotal moments in scientific history. Perfect for summer listening, this episode is a reminder that the best ideas sometimes come when we step away from the desk. THREE KEY TAKEAWAYS

Why Darwin’s voyage aboard the HMS Beagle was never meant to be a scientific breakthrough—but became one anyway.

How observation, curiosity, and a break from routine led to one of the most powerful theories in science.

What Darwin’s journey teaches us about creativity, fieldwork, and the value of stepping outside your comfort zone.

Resources & Further Reading:

• Darwin Online – The Complete Works of Charles Darwin

• Smithsonian Magazine: Darwin’s Life on the Beagle

• Galápagos Conservancy – Science and Conservation

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

Let’s Connect!

Website: mathsciencehistory.com Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social Instagram: https://www.instagram.com/math.science.history

If you love Math, Science, History, here’s how you can help:🌟 Leave a review – It helps more people discover the show!📢 Share this episode with friends & fellow history buffs!🔔 Subscribe on your favorite podcast platform

☕ Support the Show: Coffee!! PayPal

🛍 Checking out our merch: https://www.mathsciencehistory.com/the-store

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

Until next time, carpe diem!

Leonardo da Vinci is often remembered for the Mona Lisa and The Last Supper—but he was so much more than a painter. In this episode, we uncover the Renaissance icon’s groundbreaking work in engineering, anatomy, and invention, as well as explore the quieter truths of his personal identity.

We ask a powerful question: What might the world look like if everyone—regardless of gender or sexuality—could live and create as freely as Leonardo did, without fear of judgment?

Join us as we journey through Leonardo’s notebooks, his unconventional relationships, and the brilliance he left behind—not just in paint, but in thought.

 

THREE KEY TAKE-AWAYS

How Leonardo’s engineering and scientific contributions shaped modern innovations—from anatomy to flight.

Insight into Leonardo’s personal life, including his relationships with Salaì and Melzi, and what modern historians believe about his sexuality.

A broader question of what happens when people are allowed to live and create authentically—without fear of shame or suppression.

Resources & References

Walter Isaacson’s biography of Leonardo da Vinci: https://www.simonandschuster.com/books/Leonardo-da-Vinci/Walter-Isaacson/9781501139154

Leonardo da Vinci’s notebooks (Codex Atlanticus): https://www.leonardodigitale.com

Museum of Science, Leonardo DaVinci

Leonardo da Vinci’s mother was a slave, according to new research

Da Vinci's mother was an enslaved teenager trafficked to Italy, new documents suggest

Leonardo’s letter to Ludovico Sforza

10 of Leonardo da Vinci’s Most Important Inventions

Leonardo daVinci – by Walter Isaacson

The Victoria and Albert Museum – Leonardo daVinci’s Codices

 

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

Let’s Connect!

Website: mathsciencehistory.com Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social Instagram: https://www.instagram.com/math.science.history

If you love Math, Science, History, here’s how you can help:🌟 Leave a review – It helps more people discover the show!📢 Share this episode with friends & fellow history buffs!🔔 Subscribe on your favorite podcast platform

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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

🎵 Audio: Mixed by David Aviles Until next time, carpe diem!

Episode Overview: Did people in antiquity ever go on vacation? The short answer is yes—and the long answer is a fascinating journey through Roman villas, Greek festivals, Byzantine retreats, Tang dynasty poetry, and sacred pilgrimages. In this Flashcard Friday episode, Gabrielle Birchak uncovers how the privileged, the pious, and the poetic found ways to take breaks, explore new places, and seek leisure across 1,400 years of ancient history. From Pliny the Younger’s coastal villa to early travel writing in Baghdad, we’ll explore how the idea of “getting away” is as old as civilization itself.

Three Things Listeners Will Learn:

1. How ancient Romans and Greeks viewed leisure and travel.

2. How pilgrimage functioned as early tourism across Christian and Islamic worlds.

3. What writings from antiquity reveal about humanity’s timeless desire to escape daily routines.

 

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

Let’s Connect!

www.Instagram.com/math.science.history

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https://www.threads.com/@math.science.history

Enjoying the Podcast?

If you love Math, Science, History, here’s how you can help: Leave a review – It helps more people discover the show! Share this episode with friends & fellow history buffs! Subscribe on your favorite podcast platform

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Checking out our merch: https://www.mathsciencehistory.com/the-store

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

Until next time, carpe diem!

In this special Pride Month episode, Gabrielle explores the fascinating world of queerness in nature. From same-sex penguin pairs in New York to gender-changing clownfish in coral reefs, nature has always been more diverse, adaptable, and surprising than human categories suggest. Drawing on over 600 years of scientific observation, this episode takes listeners on a global journey through the history of animal research, challenges long-held myths, and reflects on what science teaches us about identity and diversity today.

3 Things Listeners Will Learn:

How scientists from Aristotle to today have observed same-sex and gender-diverse behaviors in animals.

Why queerness in nature offers evolutionary advantages, from social bonding to population resilience.

How modern research is reshaping our understanding of sexual and gender diversity across species.

Resources & References

Evolution's Rainbow by Joan Roughgarden

Biological Exuberance by Bruce Bagemihl

Sexual Selections: What We Can and Can’t Learn About Sex from Animals by Marlene Zuk

Scientific American: “Bisexual Species: Unorthodox Sex in the Animal Kingdom”

National Wildlife Federation: "Same-Sex Behavior Among Animals Isn’t New. Science Is Finally Catching Up"

 

🔗 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

 

🌍 Let’s Connect!

Website: mathsciencehistory.com Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social Instagram: https://www.instagram.com/math.science.history

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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 Now You Are Here by Sergey Cheremisiniv Eternal Love by Kris Keypovsky A Journey Beyond by Christian Bodhi

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Episode Overview:

In this Flashcard Friday episode of Math! Science! History!TM  Gabrielle breaks down the powerful numbers behind the misinformation and legislative attacks targeting LGBTQ+ and especially transgender communities in the United States. With over 550 anti-LGBTQ+ bills introduced across 49 states in 2023 alone, it's time to ask: What does the data actually say?

From the percentage of Americans who identify as LGBTQ+ to the hard truth about who actually commits acts of harm, this episode unpacks the math that shatters the myths. Because when fear leads, facts must speak louder.

3 Things You'll Learn in This Episode:

1. What percentage of the U.S. population identifies as LGBTQ+ and how small the transgender community actually is.

2. Who is statistically responsible for most sexual violence—and how trans people are often the victims, not perpetrators.

3. Which states introduced the most anti-LGBTQ+ bills in 2023, and what types of legislation are being proposed.

Resources

Gallup: LGBTQ+ Identification Rises to 7.6% in U.S.

UCLA Williams Institute: Transgender Population Estimates

The Trevor Project: 2023 National Survey on LGBTQ Youth Mental Health

ACLU: Legislative Attacks on LGBTQ Rights

Trans Murder Monitoring Report (TGEU)

 

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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Enjoying the Podcast?

If you love Math, Science, History, here’s how you can help: Leave a review – It helps more people discover the show! Share this episode with friends & fellow history buffs! Subscribe on your favorite podcast platform

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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

Until next time, carpe diem!

Episode Overview: Long before Europe adopted the concept of zero, the ancient Maya had already created one of the most sophisticated mathematical systems in the world. In this episode of Math Science History, host Gabrielle Birkjak uncovers the secrets of  Mayan mathematics, from the elegance of their base-20 number system, to their revolutionary use of zero, to the celestial precision encoded in the Dresden Codex.

We explore how the Maya embedded math into everything from pyramids to calendars, and how European scholars like Ernst Förstemann helped rediscover their brilliance centuries later. This isn’t just a story about numbers, it’s a story about worldview, time, astronomy, and one of the most advanced mathematical traditions of the ancient world.

Three Things You’ll Learn in This Episode:How the ancient Maya independently invented and used zero in a positional number system.

Why their base-20 (vigesimal) system was uniquely suited for astronomy and calendar cycles.

How the Dresden Codex survived colonialism and war to become a key to understanding Mayan math and astronomy.

Resources and Further Reading:

SLUB Dresden Digital Archive: View the Dresden Codex: https://digital.slub-dresden.de/werkansicht/dlf/29691/1

Förstemann, Ernst. Commentary on the Maya Manuscript in the Royal Public Library of Dresden (1901): https://archive.org/details/commentarymaya00fruoft

Coe, Michael D., and Stephen Houston. The Maya, 9th ed. Thames & Hudson, 2015.

Ifrah, Georges. The Universal History of Numbers. Wiley, 2000.

British Museum, Maya Mathematics Learning Resource: https://www.britishmuseum.org/learn/schools/ages-7-11/maths/maya-mathematics

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

 

Let’s Connect!

Website: mathsciencehistory.com Bluesky: https://bsky.app/profile/mathsciencehistory.bsky.social Instagram: https://www.instagram.com/math.science.history  

Enjoying the Podcast?

If you love Math, Science, History, here’s how you can help: Leave a review – It helps more people discover the show! Share this episode with friends & fellow history buffs! Subscribe on your favorite podcast platform

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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 🎵 Audio mixed by David Aviles

Until next time, carpe diem!

Ever find yourself squinting at a metric label, trying to figure out how much a liter is in cups—or how heavy your suitcase is in pounds? In this episode of Math! Science! History!, host Gabrielle Birchak shares fast, intuitive tricks to help you convert metric units, without numbers, calculators, or charts.

Through rhythm, storytelling, and everyday comparisons, you’ll learn how to feel conversions in your head, whether you’re driving, walking, or cooking. From chocolate bars and milk jugs to cat weights and yoga mats, we’re turning complex conversions into simple, memorable cues. This episode is perfect for anyone who wants to sharpen their mental math, and sound like a genius without pulling out their phone.

3 Things You'll Learn in This Episode:

- How to mentally visualize metric conversions using sensory and familiar objects—no math required.- Real-world reference points for converting volume, weight, distance, and temperature.- Simple memory tricks to help internalize metric vs. imperial conversions while on the go.

Resources Mentioned:Metric System Overview – National Institute of Standards and Technology (NIST) Quick Conversion Tables – Metric Conversions 3 Simple Tricks For Converting Metric Units In Your Head

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

Let’s Connect!

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Enjoying the Podcast?

If you love Math! Science! History! here’s how you can help: Leave a review – It helps more people discover the show! Share this episode with friends & fellow history buffs! Subscribe on your favorite podcast platform

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Checking out our merch: https://www.mathsciencehistory.com/the-store

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

Until next time, carpe diem!