There are times in mathematics when we are generalizing the behavior of many different, but similar, entities. One such time that this happens is the use cases of Big O notation, which include describing the long-term behavior of functions, and talking about how accurate numerical calculations are. On this problem episode, we are going to discuss Big O notation and how to use it.

This episode is licensed by Sofia Baca under a Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.
[Featuring: Sofía Baca]

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P12: O My God (Big O Notation)

Hosted by Gabriel Hesch and Autumn Phaneuf, who have advanced degrees in EE and industrial engineering/operations research respectively, come together to discuss mathematics as a pure field al in its own as well as how it describes the language of science, engineering, and even creativity. &nbsp;

Breaking Math brings you the absolute best in interdisciplinary science discussions - &nbsp;bringing together experts in varying fields including artificial intelligence, neuroscience, evolutionary biology, physics, chemistry and materials-science, and more - &nbsp;to discuss where humanity is headed. website: &nbsp;breakingmath.io&nbsp; linktree: &nbsp;linktree.com/breakingmathmedia email: &nbsp;breakingmathpodcast@gmail.com

Science

Mathematics

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, [https://www.discovermagazine.com/author/snadis/1] the author of the book 'The Gravity of Math [https://www.hachettebookgroup.com/titles/steve-nadis/the-gravity-of-math/9781541604292/].' 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

94. Interview with Steve Nadis, Co-author of 'Gravity of Math'

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 [https://www.youtube.com/@RayKitty]. (Find out more about the Ray Kitty Creation Workshop by clicking here [https://mrdave.raykitty.com/]).  

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 Universe [https://www.hachettebookgroup.com/titles/steve-nadis/the-gravity-of-math/9781541604292/] by Dr. Shing-Tung Yau and Steve Nadis.    This book is all about the history of our understanding of gravity from the theories of Isaac Newton to Albert Einstein and beyond, including gravitational waves, black holes, as well as some of the current uncertainties regarding a precise definition of mass.  On sale now!  
 * EVERYTHING IS PREDICTABLE: How Bayesian Statistics Explain Our World [https://www.netgalley.com/widget/516523/redeem/23dc460e436c2d0582e559b4d84ee909cf774accba78999f2291a8f97813bae0] by Tom Chivers.  Published by Simon and Schuster.   This book explains the importance of Baye's Theorem in helping us to understand why  highly accurate screening tests can lead to false positives, a phenomenon we saw during the Covid-19 pandemic; How a failure to account for Bayes' Theorem has put innocent people in jail; How military strategists using the theorem can predict where an enemy will strike next, and how Baye's Theorem is helping us to understang machine learning processes - a critical skillset to have in the 21st century.
   Available 05/07/2024
 * A CITY ON MARS: Can we settle space, should we settle space, and have we really thought this through? [https://www.penguinrandomhouse.com/books/639449/a-city-on-mars-by-kelly-and-zach-weinersmith/]  by authors Dr. Kelly and Zach Weinersmith.  Zach Weinersmith is the artist and creator of the famous cartoon strip Saturday Morning Breaking Cereal [https://www.smbc-comics.com/]!  
   
   We've got a lot of great episodes coming up!  Stay tuned.

93. The 10,000 Year Problem (feat. David Gibson of Ray Kitty Creation Workship)

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 [https://twitter.com/breakingmathpod]

Follow us on Instagram:  @Breaking Math Media [https://www.instagram.com/breakingmathmedia/]

Email us:  BreakingMathPodacst@gmail.com

92. The Mathematical Heart of Games Explored with Prof. du Sautoy

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 [https://www.tiktok.com/@bearbaitofficial] and YouTube [https://www.youtube.com/@bearbaitofficial] 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 [https://zen.ai/1e7eBWWMLcSL_G10VxiSlQ]

91.  Brain Organelles, AI, and Other Scary Science - An Interview with GT (Part 2)

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 [https://pubs.rsc.org/en/content/articlelanding/2024/dd/d3dd00077j] 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

 * Interactive theorem provers can revolutionize the way scientific theories are formulated and verified, ensuring mathematical certainty and minimizing errors.
 * Interactive theorem provers require a high level of mathematical knowledge and may not be accessible to all scientists and engineers.
 * Formal verification using interactive theorem provers can eliminate human error and hidden assumptions, leading to more confident and reliable scientific findings.
 * Interactive theorem provers promote clear communication and collaboration across disciplines by forcing explicit definitions and minimizing ambiguities in scientific language. Lean Theorem Provers enable scientists to construct modular and reusable proofs, accelerating the pace of knowledge acquisition.
 * Formal verification presents challenges in terms of transforming informal proofs into a formal language and bridging the reality gap.
 * Integration of theorem provers and machine learning has the potential to enhance creativity, verification, and usefulness of machine learning models.
 * The limitations and variables in formal verification require rigorous validation against experimental data to ensure real-world accuracy.
 * Lean Theorem Provers have the potential to provide unwavering trust, accelerate innovation, and increase accessibility in scientific research.
 * AI as a scientific partner can automate the formalization of informal theories and suggest new conjectures, revolutionizing scientific exploration.
 * The impact of Lean Theorem Provers on humanity includes a shift in scientific validity, rapid scientific breakthroughs, and democratization of science. 

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P12: O My God (Big O Notation)

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