Flash Forward is a show about possible (and not so possible) future scenarios. What would the warranty on a sex robot look like? How would diplomacy work if we couldn’t lie? Could there ever be a fecal transplant black market? (Complicated, it wouldn’t, and yes, respectively, in case you’re curious.) Hosted and produced by award winning science journalist Rose Eveleth, each episode combines audio drama and journalism to go deep on potential tomorrows, and uncovers what those futures might re ...
…
continue reading
Content provided by Gabrielle Birchak. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Gabrielle Birchak or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://ppacc.player.fm/legal.
Similar to Math Science History with Gabrielle Birchak
DNA science. Artificial intelligence. Smartphones and 3D printers. Science and technology have transformed the world we live in. But how did we get here? It wasn’t by accident. Well, sometimes it was. It was also the result of hard work, teamwork, and competition. And incredibly surprising moments. Hosted by bestselling author Steven Johnson (“How We Got To Now”), American Innovations uses immersive scenes to tell the stories of the scientists, engineers, and ordinary people behind the great ...
…
continue reading
Come dive into one of the curiously delightful conversations overheard at National Geographic’s headquarters, as we follow explorers, photographers, and scientists to the edges of our big, weird, beautiful world. Hosted by Peter Gwin and Amy Briggs.
…
continue reading
Science Friction's latest series is: Cooked. We dig into food science pickles. Why are studies showing that ice cream could be good for you? Do we really need as many electrolytes as the internet says? And why are people feeling good on the carnivore diet? Nutrition and food scientist Dr Emma Beckett takes us through what the evidence says about foods like meat, ice cream and potatoes — and unpicks why nutrition studies can be so conflicting and confusing. All six episodes of Cooked are avai ...
…
continue reading
America is divided, and it always has been. We're going back to the moment when that split turned into war. This is Uncivil: Gimlet Media's new history podcast, hosted by journalists Jack Hitt and Chenjerai Kumanyika. We ransack the official version of the Civil War, and take on the history you grew up with. We bring you untold stories about covert operations, corruption, resistance, mutiny, counterfeiting, antebellum drones, and so much more. And we connect these forgotten struggles to the ...
…
continue reading
In 1997, thirty-nine people took their own lives in an apparent mass suicide. The events captivated the media and had people across the planet asking the same question... ‘Why?’ 20 years later, those who lost loved ones and those who still believe - tell their story. Hosted by Glynn Washington of Snap Judgment. "Heaven's Gate: The Cult of Cults," is now a four-part docuseries inspired by this podcast, streaming on HBO Max.
…
continue reading
As She Rises brings together local poets and activists from throughout North America to depict the effects of climate change on their home and their people. Each episode carries the listener to a new place through a collection of voices, local recordings and soundscapes. Stories span from the Louisiana Bayou, to the tundras of Alaska to the drying bed of the Colorado River. Centering the voices of native women and women of color, As She Rises personalizes the elusive magnitude of climate cha ...
…
continue reading
Stephen Fry's 7 Deady Sins - I will take each one of the Seven Sins in turn, lay them out on the surgical table and poke, prod, pry and provoke in an attempt to try to anatomise and understand them; I hope and believe it will be, if nothing else, delicious fun and something of a change from the usual run of podcastery. Hosted on Acast. See acast.com/privacy for more information.
…
continue reading
Tim Harford and the More or Less team try to make sense of the statistics which surround us. From BBC Radio 4
…
continue reading
Interviews with mathematics education researchers about recent studies. Hosted by Samuel Otten, University of Missouri. www.mathedpodcast.com Produced by Fibre Studios
…
continue reading
Player FM - Podcast App
Go offline with the Player FM app!
Go offline with the Player FM app!
))
FLASHCARDS: Math, Logic, and Paradoxes Explained
Manage episode 480203589 series 2737493
Content provided by Gabrielle Birchak. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Gabrielle Birchak or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://ppacc.player.fm/legal.
Episode Overview
In this episode of Math, Science, History, host Gabrielle Birchak unpacks the deep connection between math and logic. From the foundations of reasoning to Euclid’s cookie-themed proof of infinite primes and the mind-bending Russell's Paradox, you’ll explore how logic shapes the very core of mathematics. Whether you're a math lover, teacher, or curious thinker, this episode will challenge the way you see numbers and arguments.
What You’ll Learn:
- Why logic is the foundation of all mathematical proof and reasoning.
- The clever logic behind Euclid’s timeless proof of infinite prime numbers.
- How paradoxes like Russell’s exposed the limits of early set theory and reshaped modern math.
Links & Resources:
An Introduction to Mathematical Logic by Richard E. Hodel This book offers a comprehensive introduction to the fundamental concepts of mathematical logic, making it suitable for beginners and those looking to solidify their understanding.
Proofs and Refutations by Imre Lakatos Presented as a series of dialogues, this classic work explores the philosophy of mathematics and the process of mathematical discovery, challenging readers to think critically about proofs and the evolution of mathematical ideas.
The Laws of Thought by George Boole This seminal work lays the foundation for Boolean algebra, delving into the relationship between logic and mathematics, and is essential reading for those interested in the logical structures underpinning mathematical reasoning.
Introduction to Mathematical Logic by Elliott Mendelson Renowned for its clarity and depth, this text covers various aspects of mathematical logic, including set theory and computability, and is highly recommended for those seeking a rigorous exploration of the subject.
Logic: A Very Short Introduction by Graham Priest This concise guide provides an engaging overview of logic, touching upon its philosophical implications and practical applications, making it a great starting point for listeners new to the topic.
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!
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
☕ Support the Show
If you’d like to support Math, Science, History, consider:Checking out our merch: https://www.mathsciencehistory.com/the-store
Sponsored By: Coffee!! https://shorturl.at/bHIsc
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!
115 episodes
Share
Manage episode 480203589 series 2737493
Content provided by Gabrielle Birchak. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Gabrielle Birchak or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://ppacc.player.fm/legal.
Episode Overview
In this episode of Math, Science, History, host Gabrielle Birchak unpacks the deep connection between math and logic. From the foundations of reasoning to Euclid’s cookie-themed proof of infinite primes and the mind-bending Russell's Paradox, you’ll explore how logic shapes the very core of mathematics. Whether you're a math lover, teacher, or curious thinker, this episode will challenge the way you see numbers and arguments.
What You’ll Learn:
- Why logic is the foundation of all mathematical proof and reasoning.
- The clever logic behind Euclid’s timeless proof of infinite prime numbers.
- How paradoxes like Russell’s exposed the limits of early set theory and reshaped modern math.
Links & Resources:
An Introduction to Mathematical Logic by Richard E. Hodel This book offers a comprehensive introduction to the fundamental concepts of mathematical logic, making it suitable for beginners and those looking to solidify their understanding.
Proofs and Refutations by Imre Lakatos Presented as a series of dialogues, this classic work explores the philosophy of mathematics and the process of mathematical discovery, challenging readers to think critically about proofs and the evolution of mathematical ideas.
The Laws of Thought by George Boole This seminal work lays the foundation for Boolean algebra, delving into the relationship between logic and mathematics, and is essential reading for those interested in the logical structures underpinning mathematical reasoning.
Introduction to Mathematical Logic by Elliott Mendelson Renowned for its clarity and depth, this text covers various aspects of mathematical logic, including set theory and computability, and is highly recommended for those seeking a rigorous exploration of the subject.
Logic: A Very Short Introduction by Graham Priest This concise guide provides an engaging overview of logic, touching upon its philosophical implications and practical applications, making it a great starting point for listeners new to the topic.
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!
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
☕ Support the Show
If you’d like to support Math, Science, History, consider:Checking out our merch: https://www.mathsciencehistory.com/the-store
Sponsored By: Coffee!! https://shorturl.at/bHIsc
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!
115 episodes
All episodes
×
Welcome to Player FM!
Player FM is scanning the web for high-quality podcasts for you to enjoy right now. It's the best podcast app and works on Android, iPhone, and the web. Signup to sync subscriptions across devices.
Similar to Math Science History with Gabrielle Birchak
Flash Forward is a show about possible (and not so possible) future scenarios. What would the warranty on a sex robot look like? How would diplomacy work if we couldn’t lie? Could there ever be a fecal transplant black market? (Complicated, it wouldn’t, and yes, respectively, in case you’re curious.) Hosted and produced by award winning science journalist Rose Eveleth, each episode combines audio drama and journalism to go deep on potential tomorrows, and uncovers what those futures might re ...
…
continue reading
DNA science. Artificial intelligence. Smartphones and 3D printers. Science and technology have transformed the world we live in. But how did we get here? It wasn’t by accident. Well, sometimes it was. It was also the result of hard work, teamwork, and competition. And incredibly surprising moments. Hosted by bestselling author Steven Johnson (“How We Got To Now”), American Innovations uses immersive scenes to tell the stories of the scientists, engineers, and ordinary people behind the great ...
…
continue reading
Come dive into one of the curiously delightful conversations overheard at National Geographic’s headquarters, as we follow explorers, photographers, and scientists to the edges of our big, weird, beautiful world. Hosted by Peter Gwin and Amy Briggs.
…
continue reading
Science Friction's latest series is: Cooked. We dig into food science pickles. Why are studies showing that ice cream could be good for you? Do we really need as many electrolytes as the internet says? And why are people feeling good on the carnivore diet? Nutrition and food scientist Dr Emma Beckett takes us through what the evidence says about foods like meat, ice cream and potatoes — and unpicks why nutrition studies can be so conflicting and confusing. All six episodes of Cooked are avai ...
…
continue reading
America is divided, and it always has been. We're going back to the moment when that split turned into war. This is Uncivil: Gimlet Media's new history podcast, hosted by journalists Jack Hitt and Chenjerai Kumanyika. We ransack the official version of the Civil War, and take on the history you grew up with. We bring you untold stories about covert operations, corruption, resistance, mutiny, counterfeiting, antebellum drones, and so much more. And we connect these forgotten struggles to the ...
…
continue reading
In 1997, thirty-nine people took their own lives in an apparent mass suicide. The events captivated the media and had people across the planet asking the same question... ‘Why?’ 20 years later, those who lost loved ones and those who still believe - tell their story. Hosted by Glynn Washington of Snap Judgment. "Heaven's Gate: The Cult of Cults," is now a four-part docuseries inspired by this podcast, streaming on HBO Max.
…
continue reading
As She Rises brings together local poets and activists from throughout North America to depict the effects of climate change on their home and their people. Each episode carries the listener to a new place through a collection of voices, local recordings and soundscapes. Stories span from the Louisiana Bayou, to the tundras of Alaska to the drying bed of the Colorado River. Centering the voices of native women and women of color, As She Rises personalizes the elusive magnitude of climate cha ...
…
continue reading
Stephen Fry's 7 Deady Sins - I will take each one of the Seven Sins in turn, lay them out on the surgical table and poke, prod, pry and provoke in an attempt to try to anatomise and understand them; I hope and believe it will be, if nothing else, delicious fun and something of a change from the usual run of podcastery. Hosted on Acast. See acast.com/privacy for more information.
…
continue reading
Tim Harford and the More or Less team try to make sense of the statistics which surround us. From BBC Radio 4
…
continue reading
Interviews with mathematics education researchers about recent studies. Hosted by Samuel Otten, University of Missouri. www.mathedpodcast.com Produced by Fibre Studios
…
continue reading
Player FM - Podcast App
Go offline with the Player FM app!
Go offline with the Player FM app!
