Breaking Math Podcast
Gabriel Hesch
Breaking Math brings you the absolute best in interdisciplinary science discussions - bringing together experts in varying fields including artificial intelligence, neuroscience, evolutionary biology, physics, chemistry and materials-science, and more - to discuss where humanity is headed.
** Includes helpful information for STEM students such as scholarship opportunities, free and cheap resources such as textbooks, open source material, recommended lectures on YouTube, School-to-Career pipeline tips and more! Subscribe to our newsletter on our website below:
website: breakingmath.io
linktree: linktree.com/breakingmathmedia
email: breakingmatnpodcast@gmail.com
Kategorien: Nachrichten und Politik
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Help Support The Podcast by clicking on the links below: * Try out ZenCastr w/ 30% Discount [https://zen.ai/1e7eBWWMLcSL_G10VxiSlQ]Use my special link [https://zen.ai/1e7eBWWMLcSL_G10VxiSlQ] to save 30% off your first month of any Zencastr paid plan * Patreon [https://www.patreon.com/breakingmath] * YouTube [https://www.youtube.com/@breakingmathpod] * Breaking Math Website [http://breakingmath.io/]Email us for copies of the transcript! Resources on the LEAN theorem prover and programming language can be found at the bottom of the show notes (scroll to the bottom). Summary 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 scienc
Vorherige Folgen
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131 - 90. LEAN Theorem Provers used to model Physics and Chemistry Sat, 16 Mar 2024
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130 - 89. Brain Organelles, AI, and the Other Scary Science - An Interview with GT (Part I) Tue, 05 Mar 2024
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129 - 88. Can OpenAi's SORA learn and model real-world physics? (Part 1 of n) Tue, 27 Feb 2024
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128 - 87. OpenAi SORA, Physics-Informed ML, and a.i. Fraud- Oh My! Tue, 20 Feb 2024
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127 - 86. Math, Music, and Artificial Intelligence - Levi McClain Interview (Final Part) Sun, 18 Feb 2024
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126 - 85. Math, Music, Neuroscience, and Fear - an Interview with Musician Levi McClain Tue, 13 Feb 2024
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125 - 84. (Part 2) Intelligence in Nature v. Machine Learning - an Interview with Brit Cruise Tue, 06 Feb 2024
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124 - 83. Intelligence in Nature v. Machine Learning-An Interview with Brit Cruise - Part 1 of 2 Tue, 30 Jan 2024
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123 - A.I. and Materials Discovery - an Interview with Taylor Sparks Sun, 21 Jan 2024
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122 - In Memory of Sofia Baca, Cofounder and cohost of Breaking Math Thu, 11 Jan 2024
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121 - 81: Correct. Now Try Again (Multiple Approaches to the Same Problem) Mon, 24 Jul 2023
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120 - 80: Physical Dimension (Dimensional Analysis) Mon, 26 Jun 2023
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119 - 79: 1 2 3 (Counting) Thu, 08 Jun 2023
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118 - 78: Perpetual Notion (Entropy and Thermodynamics) Tue, 09 May 2023
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117 - 77: An Interview with Christopher Roblesz of MathNMore Tue, 28 Feb 2023
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116 - 76: Joule Pay for This! (Energy) Sun, 15 Jan 2023
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115 - 75: Existential Physics with Sabine Hossenfelder (Author Interview) Thu, 13 Oct 2022
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114 - 74: Lights, Camera, Action! (3D Computer Graphics: Part I) Sun, 19 Jun 2022
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113 - 73: Materialism: a Material Science Podcast Podcast Episode (Interview with Taylor Sparks) Sat, 28 May 2022
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112 - 72: The Lifestyles of the Mathematical and Famous (an Interview with Author Robert Black) Sun, 15 May 2022
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111 - 71: What's the Matter? An Interview with Chris Cogswell of the Mad Scientist Podcast (Material Science) Tue, 12 Apr 2022
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110 - 70.1: Episode 70.1 of Breaking Math Podcast (Self-Reference) Sun, 20 Mar 2022
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109 - 70: This Episode Intentionally Left Blank Sat, 19 Mar 2022
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108 - Season 4 Announcement (and a Rerun of Forbidden Formulas) Sun, 20 Feb 2022
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107 - Rerun of P1: Peano Addition Thu, 27 Jan 2022
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106 - 69: An Interview with Michael Brooks, Author of "The Art of More: How Mathematics Created Civilization" Sun, 23 Jan 2022
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105 - P12: O My God (Big O Notation) Tue, 04 Jan 2022
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104 - 68: LOL!!! SO RANDOM (Random Variables) Thu, 23 Dec 2021
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103 - 67: Wrath of Math (Mathematics Used Unwisely) Thu, 09 Dec 2021
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102 - P11: Feeling Lucky? (Probability and Intuition) Tue, 30 Nov 2021
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100 - 66: Hayhoe, Let's Go! (An Interview With Climate Scientist Katharine Hayhoe) Sun, 21 Nov 2021
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99 - P10: Chivalry is Dead (Knights and Knaves #1) Sun, 14 Nov 2021
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98 - 65: An Interview with Author Ian Stewart (Book About Everyday Math) Sun, 24 Oct 2021
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97 - 64: What Projection Is This? (Map Projections) Wed, 29 Sep 2021
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96 - RR36: The Most Boring Episode Ever (Rerun: Math Games) Sun, 19 Sep 2021
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95 - 63: Broken Voting Systems (Voting Systems and Paradoxes) Sun, 05 Sep 2021
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94 - 62: The Atom Bomb of Information Operations (An Interview with John Fuisz of Veriphix) Sun, 22 Aug 2021
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93 - RR38: The Great Stratagem Heist (Game Theory: Iterated Elimination of Dominated Strategies) Sun, 23 May 2021
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92 - 61: Look at this Graph! (Graph Theory) Sun, 25 Apr 2021
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91 - P9: Give or Take (Back-of-the-Envelope Estimates / Fermi Problems) Mon, 19 Apr 2021
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90 - 60: HAMILTON! [But Not the Musical] (Quaternions) Sat, 03 Apr 2021
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89 - 59: A Good Source of Fibers (Fiber Bundles) Sun, 21 Mar 2021
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88 - 58: Bringing Curvy Back (Gaussian Curvature) Wed, 03 Mar 2021
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87 - P8: Tangent Tango (Morikawa's Recently Solved Problem) Thu, 25 Feb 2021
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86 - P7: Root for Squares (Irrationality of the Square Root of Two) Sun, 07 Feb 2021
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85 - 57: You Said How Much?! (Measure Theory) Mon, 01 Feb 2021
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84 - P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry) Thu, 28 Jan 2021
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83 - 56: More Sheep than You Can Count (Transfinite Cardinal Numbers) Sun, 24 Jan 2021
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82 - 55: Order in the Court (Transfinite Ordinal Numbers) Thu, 14 Jan 2021
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81 - 54: Oodles (Large Numbers) Mon, 21 Dec 2020