Breaking Math Podcast

Summary **Tensor Poster - If you are interested in the Breaking Math Tensor Poster on the mathematics of General Relativity, email us at BreakingMathPodcast@gmail.com In this episode, Gabriel Hesch and Autumn Phaneuf interview Steve Nadis, the author of the book 'The Gravity of Math.' They discuss the mathematics of gravity, including the work of Isaac Newton and Albert Einstein, gravitational waves, black holes, and recent developments in the field. Nadis shares his collaboration with Shing-Tung Yau and their journey in writing the book. They also talk about their shared experience at Hampshire College and the importance of independent thinking in education. In this conversation, Steve Nadis discusses the mathematical foundations of general relativity and the contributions of mathematicians to the theory. He explains how Einstein was introduced to the concept of gravity by Bernhard Riemann and learned about tensor calculus from Gregorio Ricci and Tullio Levi-Civita. Nadis also explores Einstein's discovery of the equivalence principle and his realization that a theory of gravity would require accelerated motion. He describes the development of the equations of general relativity and their significance in understanding the curvature of spacetime. Nadis highlights the ongoing research in general relativity, including the detection of gravitational waves and the exploration of higher dimensions and black holes. He also discusses the contributions of mathematician Emmy Noether to the conservation laws in physics. Finally, Nadis explains Einstein's cosmological constant and its connection to dark energy. Chapters 00:00 Introduction and Book Overview 08:09 Collaboration and Writing Process 25:48 Interest in Black Holes and Recent Developments 35:30 The Mathematical Foundations of General Relativity 44:55 The Curvature of Spacetime and the Equations of General Relativity 56:06 Recent Discoveries in General Relativity 01:06:46 Emmy Noether's Contributions to Conservation Laws 01:13:48 Einstein's Cosmological Constant and Dark Energy

Summary: The episode discusses the 10,000 year dilemma, which is a thought experiment on how to deal with nuclear waste in the future. Today's episode is hosted by guest host David Gibson, who is the founder of the Ray Kitty Creation Workshop. (Find out more about the Ray Kitty Creation Workshop by clicking here). Gabriel and Autumn are out this week, but will be returning in short order with 3 separate interviews with authors of some fantastic popular science and math books including: The Gravity of Math: How Geometry Rules the UniverseEVERYTHING IS PREDICTABLE: How Bayesian Statistics Explain Our Worldby Tom Chivers. Published by Simon and Schuster. This book explains the importance of Baye's Theorem in helping us to understand why Available 05/07/2024A CITY ON MARS: Can we settle space, should we settle space, and have we really thought this through? by authors Dr. Kelly and Zach Weinersmith. Zach Weinersmith is the artist and creator of the famous cartoon strip Saturday Morning Breaking Cereal! We've got a lot of great episodes coming up! Stay tuned.

An interview with Prof. Marcus du Sautoy about his book Around the Wold in Eighty Games . . . .a Mathematician Unlocks the Secrets of the World's Greatest Games. Topics covered in Today's Episode: 1. Introduction to Professor Marcus du Sautoy and the Role of Games - Impact of games on culture, strategy, and learning - The educational importance of games throughout history 2. Differences in gaming cultures across regions like India and China 3. Creative Aspects of Mathematics 4. The surprising historical elements and banned games by Buddha 5. Historical and geographical narratives of games rather than rules 6. Game Theory and Education 7. Unknowable questions like thermodynamics and universe's infinity 8. Professor du Sautoy's Former Books and Collections 9. A preview of his previous books and their themes 10. Gaming Cultures and NFTs in Blockchain 11. Gamification in Education 12. The Role of AI in Gaming 13. Testing machine learning in mastering games like Go 14. Alphago's surprising move and its impact on Go strategies 15 . The future of AI in developing video game characters, plots, and environments 16. Conclusion and Giveaway Announcement *Free Book Giveaway of Around The World in 88 Games . . . by Professor Marcus Du Sautory! Follow us on our socials for details: Follow us on X: @BreakingMathPod Follow us on Instagram: @Breaking Math Media Email us: BreakingMathPodacst@gmail.com

Summary Brain Organelles, A.I. and Defining Intelligence in Nature- In this episode, we continue our fascinating interview with GT, a science content creator on TikTok and YouTube known for their captivating - and sometimes disturbing science content. GT can be found on the handle ‘@bearBaitOfficial’ on most social media channels. In this episode, we resume our discussion on Brain Organelles - which are grown from human stem cells - how they are being used to learn about disease, how they may be integrated in A.I. as well as eithical concerns with them. We also ponder what constitutes intelligence in nature, and even touch on the potential risks of AI behaving nefariously. You won't want to miss this thought-provoking and engaging discussion. 30% Off ZenCastr Discount Use My Special Link to save e 30% Off Your First Month of Any ZenCastr Paid Plan

This episode is inspired by a correspondence the Breaking Math Podcast had with the editors of Digital Discovery, a journal by the Royal Society of Chemistry. In this episode the hosts review a paper about how the Lean Interactive Theorem Prover, which is usually used as a tool in creating mathemtics proofs, can be used to create rigorous and robust models in physics and chemistry. Also - we have a brand new member of the Breaking Math Team! This episode is the debut episode for Autumn, CEO of Cosmo Labs, occasional co-host / host of the Breaking Math Podcast, and overall contributor who has been working behind the scenes on the podcast on branding and content for the last several months. Welcome Autumn! Autumn and Gabe discuss how the paper explores the use of interactive theorem provers to ensure the accuracy of scientific theories and make them machine-readable. The episode discusses the limitations and potential of interactive theorem provers and highlights the themes of precision and formal verification in scientific knowledge. This episode also provide resources (listed below) for listeners interested in learning more about working with the LEAN interactive theorem prover. Takeaways Help Support The Podcast by clicking on the links below: Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid planPatreonYouTubeBreaking Math Website

This conversation explores the topic of brain organoids and their integration with robots. The discussion covers the development and capabilities of brain organoids, the ethical implications of their use, and the differences between sentience and consciousness. The conversation also delves into the efficiency of human neural networks compared to artificial neural networks, the presence of sleep in brain organoids, and the potential for genetic memories in these structures. The episode concludes with an invitation to part two of the interview and a mention of the podcast's Patreon offering a commercial-free version of the episode. Takeaways Chapters References: Muotri Labs (Brain Organelle piloting Spider Robot) Cortical Labs (Brain Organelle's trained to play Pong) *For a copy of the episode transcript, email us at breakingmathpodcast@gmail.com Help Support The Podcast by clicking on the links below: Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan Visit our PatreonSummary:

This is a follow up on our previous episode on OpenAi's SORA. We attempt to answer the question, "Can OpenAi's SORA model real-world physics?" We go over the details of the technical report, we discuss some controversial opinoins by experts in the field at Nvdia and Google's Deep Mind. The transcript for episode is avialable below upon request. Help Support The Podcast by clicking on the links below: Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan patreon subscribe to our YouTube Channel

OpenAI's Sora, a text-to-video model, has the ability to generate realistic and imaginative scenes based on text prompts. This conversation explores the capabilities, limitations, and safety concerns of Sora. It showcases various examples of videos generated by Sora, including pirate ships battling in a cup of coffee, woolly mammoths in a snowy meadow, and golden retriever puppies playing in the snow. The conversation also discusses the technical details of Sora, such as its use of diffusion and transformer models. Additionally, it highlights the potential risks of AI fraud and impersonation. The episode concludes with a look at the future of physics-informed modeling and a call to action for listeners to engage with Breaking Math content. Takeaways Chapters 00:00 Introduction to OpenAI's Sora 04:22 Overview of Sora's Capabilities 07:08 Exploring Prompts and Generated Videos 12:20 Technical Details of Sora 16:33 Limitations and Safety Concerns 23:10 Examples of Glitches in Generated Videos 26:04 Impressive Videos Generated by Sora 29:09 AI Fraud and Impersonation 35:41 Future of Physics-Informed Modeling 36:25 Conclusion and Call to Action Help Support The Podcast by clicking on the links below: Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan Visit our PatreonContact us at breakingmathpodcast@gmail.com Summary #OpenAiSora #

Help Support The Podcast by clicking on the links below: Try out ZenCastr w/ 30% Discount Use my special link to save 30% off your first month of any Zencastr paid plan Patreon YouTubeTranscripts are available upon request. Email us at BreakingMathPodcast@gmail.com Follow us on X (Twitter) Follow us on Social Media Pages (Linktree) Visit our guest Levi McClain's Pages: youtube.com/@LeviMcClain levimcclain.com/ Summary Levi McClean discusses various topics related to music, sound, and artificial intelligence. He explores what makes a sound scary, the intersection of art and technology, sonifying data, microtonal tuning, and the impact of using 31 notes per octave. Levi also talks about creating instruments for microtonal music and using unconventional techniques to make music. The conversation concludes with a discussion on understanding consonance and dissonance and the challenges of programming artificial intelligence to perceive sound like humans do. Takeaways: Chapters 00:00 What Makes a Sound Scary 03:00 Approaching Art and Music with a Technical Mind 05:19 Sonifying Data and Turning it into Sound 08:39 Exploring Music with Microtonal Tuning 15:44 The Impact of Using 31 Notes per Octave 17:37 Why 31 Notes Instead of Any Other Arbitrary Number 19:53 Creating Instruments for Microtonal Music 21:25 Using Unconventional Techniques to Make Music 23:06 Closing Remarks and Questions 24:03 Understanding Consonance and Dissonance 25:25 Programming Artificial Intelligence to Understand Consonance and Dissonance

We are joined today by content creator Levi McClain to discuss the mathematics behind music theory, neuroscience, and human experiences such as fear as they relate to audio processing. For a copy of the episode transcript, email us at BreakingMathPodcast@gmail.com. For more in depth discussions on these topics and more, check out Levi's channels at: Patreon.com/LeviMcClain youtube.com/@LeviMcClain Tiktok.com/@levimcclain Instagram.com/levimcclainmusic Help Support The Podcast by clicking on the links below: Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan Visit our Patreon

Help Support The Podcast by clicking on the links below: Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan Visit our Patreon Part 2/2 of the interview with Brit Cruise, creator of the YouTube channel "Art of the Problem," about interesting mathematics,, electrical and computer engineering problems. In Part 1, we explored what 'intelligence' may be defined as by looking for examples of brains and proto-brains found in nature (including mold, bacteria, fungus, insects, fish, reptiles, and mammals). In Part 2, we discuss aritifical neural nets and how they are both similar different from human brains, as well as the ever decreasing gap between the two. Brit's YoutTube Channel can be found here: Art of the Problem - Brit Cruise Transcript will be made available soon! Stay tuned. You may receive a transcript by emailing us at breakingmathpodcast@gmail.com. Become a supporter of this podcast: https://www.spreaker.com/podcast/breaking-math-podcast--5545277/support.

In this episode (part 1 of 2), I interview Brit Cruise, creator of the YouTube channel 'Art of the Problem.' On his channel, he recently released the video "ChatGPT: 30 Year History | How AI learned to talk." We discuss examples of intelligence in nature and what is required in order for a brain to evolve at the most basic level. We use these concepts to discuss what artificial intelligence - such as Chat GPT - both is and is not. Help Support The Podcast by clicking on the links below: Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan Visit our Patreon

Transcripts of this episode are avialable upon request. Email us at BreakingMathPodcast@gmail.com. In this episode Gabriel Hesch interviews Taylor Sparks, a professor of material science and engineering, about his recent paper on the use of generative modeling a.i. for material disovery. The paper is published in the journal Digital Discovery and is titled 'Generative Adversarial Networks and Diffusion MOdels in Material Discovery. They discuss the purpose of the call, the process of generative modeling, creating a representation for materials, using image-based generative models, and a comparison with Google's approach. They also touch on the concept of conditional generation of materials, the importance of open-source resources and collaboration, and the exciting developments in materials and AI. The conversation concludes with a discussion on future collaboration opportunities. Takeaways Help Support The Podcast by clicking on the links below: Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan Visit our Patreon

In October of 2023, Sofia Baca passed away unexpectedly from natural causes. Sofia was one of the founders and cohosts of the Breaking Math Podcast. In this episode, host Gabriel Hesch interviews Diane Baca, mother of Sofia Baca as we talk about her passions for creativity, mathematics, science, and discovering what it means to be human. Sofia lived an exceptional life with explosive creativity, a voracious passion for mathematics, physics, computer science, and creativity. Sofia also struggled immensely with mental health issues which included substance abuse as well as struggling for a very long time understand the source of their discontent. Sofia found great happiness in connecting with other people through teaching, tutoring, and creative expression. The podcast will continue in honor of Sofia. There are many folders of ideas that Sofia left with ideas for the show or for other projects. We will continue this show with sharing some of these ideas, but also with sharing stories of Sofia - including her ideas and her struggles in hopes that others may find solace in that they are not alone in their struggles. But also in hopes that others may find inspiration in what Sofia had to offer. We miss you dearly, Sofia.

Join Sofía Baca and her guests, the host and co-host of the Nerd Forensics podcast, Millicent Oriana and Jacob Urban, as they explore what it means to be able to solve one problem in multiple ways. This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/ [Featuring: Sofía Baca; Millicent Oriana, Jacob Urban[ Help Support The Podcast by clicking on the links below: Try out ZenCastr w/ 30% Discount Use my special link to save 30% off your first month of any Zencastr paid planPatreonYouTubeBreaking Math WebsiteEmail us for copies of the transcript!

The history of mathematics, in many ways, begins with counting. Things that needed, initially, to be counted were, and often still are, just that; things. We can say we have twelve tomatoes, or five friends, or that eleven days have passed. As society got more complex, tools that had been used since time immemorial, such as string and scales, became essential tools for counting not only concrete things, like sheep and bison, but more abstract things, such as distance and weight based on agreed-upon multiples of physical artifacts that were copied. This development could not have taken place without the idea of a unit: a standard of measuring something that defines what it means to have one of something. These units can be treated not only as counting numbers, but can be manipulated using fractions, and divided into arbitrarily small divisions. They can even be multiplied and divided together to form new units. So where does the idea of a unit come from? What's the difference between a unit, a dimension, and a physical variable? And how does the idea of physical dimension allow us to simplify complex problems? All of this and more on this episode of Breaking Math. Distributed under a CC BY-SA 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/ [Featuring: Sofía Baca; Millicent Oriana, Jacob Urban] Help Support The Podcast by clicking on the links below: Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid planPatreonYouTubeBreaking Math WebsiteEmail us for copies of the transcript!

Help Support The Podcast by clicking on the links below: Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid planPatreonYouTubeBreaking Math WebsiteEmail us for copies of the transcript!Join Sofia Baca and Nerd Forensics co-host Jacob Urban as they discuss all things counting! Counting is the first arithmetic concept we learn, and we typically learn to do so during early childhood. Counting is the basis of arithmetic. Before people could manipulate numbers, numbers had to exist. Counting was first done on the body, before it was done on apparatuses outside the body such as clay tablets and hard drives. However, counting has become an invaluable tool in mathematics itself, as became apparent when counting started to be examined analytically. How did counting begin? What is the study of combinatorics? And what can be counted? All of this and more, on this episode of Breaking Math. This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (full text: https://creativecommons.org/licenses/by-sa/4.0/) [Featuring: Sofia Baca; Jacob Urban]

As you listen to this episode, you'll be exerting mental effort, as well as maybe exerting effort doing other things. The energy allowing your neurons to continually charge and discharge, as well as exert mechanical energy in your muscles and chemical energy in places like your liver and kidneys, came from the food you ate. Specifically, it came from food you chewed, and then digested with acid and with the help of symbiotic bacteria. And even if that food you're eating is meat, you can trace its energy back to the sun and the formation of the earth. Much of this was established in the previous episode, but this time we're going to explore a fundamental property of all systems in which heat can be defined. All of these structures had a certain order to them; the cow that might have made your hamburger had all the same parts that you do: stomach, lips, teeth, and brain. The plants, such as the tomatoes and wheat, were also complex structures, complete with signaling mechanisms. As you chewed that food, you mixed it, and later, as the food digested, it became more and more disordered; that is to say, it became more and more "shuffled", so to speak, and at a certain point, it became so shuffled that you'd need all the original information to reconstruct it: reversing the flow of entropy would mean converting vomit back into the original food; you'd need all the pieces. The electrical energy bonding molecules were thus broken apart and made available to you. And, if you're cleaning your room while listening to this, you are creating order only at the cost of destroying order elsewhere, since you are using energy from the food you ate. Even in industrial agriculture where from 350 megajoules of human and machine energy, often 140 gigajoules of corn can be derived per acre, a ratio of more than 400:1, the order that the seeds seem to produce from nowhere is constructed from the energy of the chaotic explosion from a nearby star. So why are the concepts of heat, energy, and disorder so closely linked? Is there a general law of disorder? And why does the second law mean you can't freeze eggs in a hot pan? All of this and more on this episode of Breaking Math. Distributed under a CC BY-SA 4.0 License (https://creativecommons.org/licenses/by-sa/4.0/) [Featuring: Sofia Baca; Millicent Oriana, Jacob Urban] Help Support The Podcast by clicking on the links below: Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid planPatreonYouTubeBreaking Math WebsiteEmail us for copies of the transcript!

Christopher Roblesz is a math educator who, until the pandemic, worked as a teacher. It was his experiences during the pandemic, and his unwavering passion for preparing disadvantaged youth for STEM careers, that eventually led him to developing mathnmore, a company focused on providing an enriched educational experience for sstudents who are preparing for these careers.More on energy and entropy next time!All of this and more on this interview episode of Breaking Math! [Featuring: Sofia Baca; Christopher Roblesz]

Join Sofia Baca and her guests Millicent Oriana from Nerd Forensics and Arianna Lunarosa as they discuss energy. The sound that you're listening to, the device that you're listening on, and the cells in both the ear you're using to listen and the brain that understands these words have at least one thing in common: they represent the consumption or transference of energy. The same goes for your eyes if you're reading a transcript of this. The waves in the ears are pressure waves, while eyes receive information in the form of radiant energy, but they both are still called "energy". But what is energy? Energy is a scalar quantity measured in dimensions of force times distance, and the role that energy plays depends on the dynamics of the system. So what is the difference between potential and kinetic energy? How can understanding energy simplify problems? And how do we design a roller coaster in frictionless physics land?[Featuring: Sofia Baca; Millicent Oriana, Arianna Lunarosa] This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. Full text here: https://creativecommons.org/licenses/by-sa/4.0/