breaking math podcast by Gabriel Hesch and Autumn Phaneuf

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the groundbreaking contributions of Florence Nightingale, highlighting her use of data and statistics to revolutionize healthcare and public health during the 19th century. Discover how her innovative use of data visualization and her perseverance against gender biases transformed modern nursing and public health policy.

Mathematics quietly shapes some of the most important decisions in public life, from redistricting and congressional apportionment to federal research funding and AI policy. In this episode, Autumn and Noah speak with Dr. Karen Saxe, Senior Vice President of Government Relations at the American Mathematical Society, about how mathematical ideas influence representation, fairness, education, and the future of research. From gerrymandering and geometric compactness to life inside the U.S. Senate and the growing policy debates around AI, Karen reveals how deeply math is woven into the systems that govern everyday life.

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the groundbreaking work of Anna Schwartz, a pioneering economist who transformed macroeconomics through data-driven research. Discover how her meticulous analysis of monetary history shaped economic policy and the legacy she left for future generations.

In this episode, Lauren Williams, professor of mathematics at Harvard University and a 2025 MacArthur Fellow, speaks about the surprising and often messy reality of mathematical research. The conversation begins with a turbulent moment in academia, when federal grants supporting her work were suddenly canceled—only months before she received the MacArthur “Genius Grant,” an unexpected recognition that allowed her to continue her research. Williams explains her work in algebraic combinatorics, illustrating how abstract mathematics can connect to real-world systems. The discussion also explores the human side of discovery, from collaborations that span continents to the strange coincidence of research papers and babies arriving the same week. Finally, the episode dives into one of the most intriguing experiments in modern mathematics: the First Proof project, which tests whether artificial intelligence can produce genuine mathematical proofs, revealing both the promise and the current limitations of AI-generated reasoning.

This Women in History Mini-Series with Dr. Victoria Bateman explores the life and contributions of Priscilla Wakefield, a revolutionary figure in financial literacy and women's empowerment during the Industrial Revolution. Wakefield's work in establishing savings banks and community insurance schemes for women highlights her belief in the practical application of mathematics for everyday life. The discussion also addresses the challenges women faced in finance during her time and her lasting impact on feminist economics.

In this conversation, Dr. Bryna Kra discusses her journey in mathematics, focusing on her research, dynamical systems, the importance of collaboration, and the role of the American Mathematical Society. She emphasizes the need for better communication within the mathematics community and the challenges it faces, particularly regarding diversity and inclusion. Bryna shares her experiences in mentoring women in mathematics and reflects on her career achievements while looking forward to future contributions in the field.

In this conversation, Ian Stewart discusses the nature of mathematical inquiry, the motivations behind problem-solving in mathematics, and the importance of storytelling in making math relatable. He explores the relationship between nature and mathematics, emphasizing how patterns in nature inspire mathematical concepts. Stewart also addresses the role of AI in mathematical discovery and the importance of choosing meaningful problems to work on. He concludes by highlighting the vital role of mathematics in society and its significant contributions to the economy.

In this conversation, Ravi Vakil discusses the beauty of mathematics, the impact of AI on the field, and the importance of human interaction in mathematical education. He emphasizes the social nature of mathematics and the potential dangers of AI-generated content flooding the mathematical community. The discussion also touches on the future of education, the role of leadership in mathematics, and the balance between mathematics and other disciplines. Throughout, Vakil encourages aspiring mathematicians to embrace the beauty and interconnectedness of the subject.

Summary

In this episode, Autumn and Noah celebrate the ninth anniversary of the Breaking Math podcast, reflecting on its journey and growth. They introduce Noah Giansiracusa as the new co-host and discuss the importance of engaging with the audience, storytelling in math, and the interdisciplinary nature of the topics they plan to cover. The conversation also touches on personal experiences, defining success in podcasting, and the dynamics of co-hosting, all while embracing their nerdy sides and fostering curiosity in their listeners.

In this episode of Breaking Math, Autumn and Nicolas Niarchos critique the "green" narrative of lithium-ion technology. Tracing the industry from its 1991 commercialization to modern geopolitical tensions, the hosts expose the exploitation and environmental degradation inherent in global mining, particularly in the Democratic Republic of the Congo. By challenging the presumed sustainability of electric vehicles, they emphasize the need for supply chain transparency and urge listeners to adopt a more informed, ethically-conscious approach to modern consumption.

In this conversation, the discussion with C. Thi Nguyen revolves around the nature of metrics, qualitative knowledge, and the duality of scoring systems, particularly in the context of climbing. The speaker shares personal experiences with climbing as a case study to illustrate how scoring systems can both enhance and detract from the experience. The conversation delves into the beauty of climbing, the subtlety of value in metrics, and the importance of savoring moments in games. It also explores the tension between purpose and game mechanics, the role of enjoyment, and the complexities of scoring systems in both games and life. Ultimately, the conversation highlights the challenges of balancing values in decision-making and the risks associated with the gamification of various aspects of life.

This conversation explores the fascinating intersection of math, physics, and art, highlighting how these disciplines inform and inspire one another. Dr. Ronald Gamble discusses his journey as a theoretical physicist and artist, emphasizing the importance of recognizing patterns in nature and the role of creativity in scientific discovery. The dialogue delves into various topics, including the significance of symmetry in physics, the visualization of complex concepts like black holes and gravitational waves, and the influence of mathematical principles on artistic expression. Ultimately, the conversation underscores the idea that art and science are deeply interconnected, each enhancing the understanding and appreciation of the other.

In this conversation, Dr. Katharina Reinecke explores the intersection of technology and culture, discussing how cultural assumptions shape the design and functionality of technology. She delves into the implications of self-driving cars, the importance of understanding diverse user experiences, and the challenges posed by a predominantly Western perspective in technology development. The discussion highlights the need for greater cultural sensitivity in technology design and the potential consequences of ignoring these differences.

This conversation delves into the life and legacy of Francis Crick, co-discoverer of the DNA structure. Dr.  Matthew Cobb, the guest, explores Crick's multifaceted personality, his poetic inspirations, collaborative nature, and his later pursuits in consciousness. The discussion also touches on the controversies surrounding his work, particularly regarding the contributions of Rosalind Franklin, and reflects on Crick's complex character, blending modern scientific thought with outdated socio-political ideas.

This conversation explores the intersection of mathematics and human experience, focusing on historical figures, philosophical debates, and the ethical implications of scientific progress. Jason Socrates Bardi discusses his book 'The Great Math War', which delves into the personal stories of mathematicians, the challenges of teaching math, and the relevance of these themes in today's world, particularly in the context of AI and misinformation.

In this conversation, Dr.Vlatko Vedral discusses the complexities of quantum mechanics and its implications for our understanding of reality. He explores the stagnation in physics, the importance of thought experiments, and the potential for new discoveries through technological advancements. Vlatko emphasizes the need for adventurous research and the role of quantum information in shaping future scientific inquiries. He also speculates on the transformative possibilities of quantum technologies and their impact on human perception.

In this conversation, Drs. Gaurav Suri and Jay Mcclelland delves into the intricate relationship between artificial intelligence and human cognition, exploring similarities and differences, the evolution of AI from rule-based systems to learning models, and the concept of emergence in both fields. The discussion also touches on the efficiency of human learning compared to AI, the role of consciousness, and the ethical implications of AI technology.

In this conversation, Dr. Caleb Scharf discusses the evolution of space exploration, drawing parallels to historical figures like Darwin. He explores the implications of humanity's expansion into space, the challenges of microgravity, and the allure of Mars as a potential habitat. Scharf emphasizes the interconnectedness of space exploration with our daily lives and the future of humanity as a dispersed entity across the solar system.

In this engaging conversation, Rachel Ignotofski discusses her new book Dinosaurs, exploring the fascination with these ancient creatures, the impact of mass extinctions, and the evolution of life on Earth. She highlights the importance of paleontology, the legacy of Mary Anning, and the artistic choices made in illustrating the book. The discussion also touches on the audience for the book, quirky anecdotes from paleontological history, and the significance of understanding deep time in relation to our current ecosystem.

In this conversation, Quico discusses the nature of gullibility and the tactics used by charlatans to exploit people's beliefs. He provides insights into various case studies, including astrology and blood types, and highlights notable charlatans like Baba Ramdev and the impact of mega churches. The discussion also covers modern scams in the crypto space and emphasizes the importance of critical thinking and awareness in navigating a world filled with misinformation and exploitation. It's made known that even the smartest scientists can be fooled by charlatans. 

In this conversation, economist Dr. Victoria Bateman discusses the critical role of women in shaping economic prosperity throughout history. She argues that women's choices, independence, and labor have been overlooked in traditional economic narratives. The discussion covers various themes, including the impact of women's marriage decisions on population control, the relationship between women's independence and technological advancements, and the historical marginalization of women in economic history. Bateman emphasizes the importance of recognizing women's contributions to economic growth and the need for policies that support women's rights and independence.

In this conversation, Marcus Du Sautoy explores the intricate relationship between mathematics and various forms of art, including music, literature, and visual arts. He discusses how mathematical concepts such as prime numbers, symmetry, and randomness influence creative processes and artistic expressions. Through examples from renowned artists like Shakespeare and Dali, Du Sautoy illustrates how mathematics serves as a blueprint for understanding and creating art, while also emphasizing the emotional and aesthetic dimensions of both fields.

In this conversation, Eugenia Cheng discusses the importance of making math accessible and engaging for everyone, particularly those who have been discouraged by traditional education methods. She emphasizes the intersection of math and art, the dangers of oversimplifying complex issues with numbers, and the need for a more nuanced understanding of equality and fairness in society. Cheng also highlights the significance of mentorship and the impact of gender dynamics in mathematics, advocating for a more inclusive approach to learning and appreciating math as a creative and thoughtful discipline.

This week’s episode isn’t our usual deep dive—it’s a behind-the-scenes update. On Monday, Breaking Math vanished from Spotify, Apple, YouTube, and more without warning. After digging in, we discovered a strange RSS glitch that merged our feed with another podcast.

In this conversation, Dr. Daryl Fairweather, chief economist at Redfin, discusses her book “Hate the Game,” that frames life and career decisions as strategic games. She emphasizes the importance of understanding economic principles to navigate personal and professional challenges, negotiate effectively, and reclaim agency in various aspects of life. Fairweather shares insights on overcoming barriers related to race and gender, the impact of information asymmetry, and the significance of designing one's own path in a competitive environment. The conversation highlights the necessity of introspection, strategic thinking, and the ability to adapt in a world that often feels rigged against certain individuals.

In this conversation, Autumn and Dr. Anthony Bonato explore the fascinating world of networks, discussing their significance in various fields, including mathematics, social interactions, and even the spread of diseases like COVID-19 in his new book Dots and Lines. Anthony shares his journey into network science, the importance of understanding networks in everyday life, and how they can reveal hidden connections. The discussion also touches on popular culture references, such as Game of Thrones and Survivor, to illustrate the practical applications of network theory. Ultimately, the conversation emphasizes the need to embrace mathematics and recognize the pervasive role of networks in our lives.

In this episode of Breaking Math, Dr. Noah Giansiracusa discusses his book 'Robin Hood Math', emphasizing the importance of mathematical literacy in navigating an algorithm-driven world. He explores how math can empower everyday people, the writing process behind his book, and practical applications of math in daily life, including social media algorithms and financial decisions. The conversation highlights the simplicity of the math that truly matters and encourages listeners to reclaim agency through understanding mathematics.

In this conversation, Dr. Christoph Bartneck discusses the intersection of swimming and computer science, exploring how mathematical patterns can enhance swim training. He introduces the concept of a formal swim markup language to improve data exchange and training efficiency. The discussion also delves into the visualization of swimming techniques, the importance of mental engagement in training, and the aesthetic appeal of mathematics. Christoph shares insights on the challenges of writing his book and his vision for creating a global community around swimming and mathematics.

In this episode of Breaking Math, Autumn explores the complex world of AI ethics, focusing on its implications in education, the accuracy of AI systems, the biases inherent in algorithms, and the challenges of data privacy. The discussion emphasizes the importance of ethical considerations in mathematics and computer science, advocating for transparency and accountability in AI systems. Autumn also highlights the role of mathematicians in addressing these ethical dilemmas and the need for society to engage critically with AI technologies.

In this episode, we explore the intricate mathematics behind Sp0tify's (ok... and other's) shuffle feature, revealing how it is designed to feel random while actually being carefully curated. We discuss the psychological implications of randomness, the Fisher-Yates shuffle algorithm, and how engineers have created a system that respects human perception of randomness. The conversation delves into the philosophical aspects of curated randomness and the broader implications of mathematical principles in technology and human experience.

This conversation explores the intricate relationship between mathematics and artificial intelligence (AI) for people who don't want to get too math heavy and want things simplified as much as possible. It delves into how algorithms, machine learning, and various mathematical tools like linear algebra, calculus, and statistics form the backbone of AI technologies. The discussion highlights real-world applications of AI, the ethical implications of its use, and the importance of mathematical literacy in an increasingly AI-driven world. Ultimately, it emphasizes that understanding the mathematical foundations of AI empowers individuals to engage meaningfully with technology and its impact on society.

This conversation delves into the intersection of quantum computing and cryptography, focusing on the implications of quantum computers for current encryption methods and the necessity for post-quantum cryptography. Dr. Dustin Moody from NIST discusses the threats posed by quantum computing, particularly through Shor's algorithm, and the ongoing efforts to develop new cryptographic standards that can withstand these threats. The discussion also covers the role of NIST in standardizing post-quantum algorithms, the mathematical challenges involved, and the importance of preparing businesses for the transition to these new systems.

In this episode,  Autumn interviews Dr. Ileana Pazos, an expert in dosimetry, discussing the critical role of radiation measurement in various industries, including healthcare and food safety. They explore the science behind dosimetry, the applications of radiation, the challenges faced in accurate measurements, and the misconceptions surrounding food irradiation. Ileana emphasizes the importance of public education and the need for global standards in radiation measurement, while also sharing her personal connection to the field and the future of radiation technologies.

In this conversation, Dr. Elizabeth Strychalski discusses the fascinating field of synthetic biology, particularly focusing on synthetic cells. She shares her journey into this research area, the challenges of defining life, and the ethical considerations surrounding synthetic biology. The conversation also explores the potential applications of synthetic cells in environmental science and medicine, as well as the importance of engineering standards and biomanufacturing for sustainability. Dr. Strychalski emphasizes the need for collaboration and communication in the scientific community to advance this field responsibly and effectively.

In this episode of Breaking Math, hosts Autumn and Gabriel explore the innovative intersections of fire science and technology with experts Amy Mensch and Ryan Falkenstein-Smith who work at NIST. They discuss the groundbreaking photoacoustic technique for measuring soot deposition, its applications in fire safety and forensic investigations, and the broader implications for fire research. The conversation highlights the importance of integrating advanced technologies into firefighting and the potential for future developments in the field.

In this episode of Breaking Math, Autumn and Andrew Novick delve into the intricate world of timekeeping, exploring the significance of precise time measurement in modern technology. They discuss the evolution from traditional atomic clocks to cutting-edge optical clocks, the critical role of time in various industries, and the implications of time on fundamental physics, including Einstein's theories. The conversation also touches on the quirky concept of leap seconds and the future advancements in timekeeping technology, emphasizing the relative nature of time and its perception.

Summary

In this episode, Dr. Destine Nock, CEO of Peoples Energy Analytics and a Professor at Carnegie Mellon University, joins Autumn to dive deep into the world of energy equity. They explore how cutting-edge data analytics are revolutionizing the landscape of affordable energy access. As the global demand for sustainable energy solutions continues to grow, the need to ensure fair and inclusive energy distribution becomes more critical than ever. Together, our hosts break down how data-driven insights are being leveraged to develop and implement policies that make energy more accessible to underserved communities, tearing down socioeconomic barriers and paving the way for a more equitable future.

In this captivating episode of Breaking Math, hosts Gabriel and Autumn dive deep into chaos theory—a fascinating branch of mathematics that explores the behavior of complex systems highly sensitive to initial conditions. They break down the butterfly effect, revealing how tiny variations can lead to major consequences and discuss the inherent unpredictability in weather forecasting and the financial markets. The episode also uncovers chaos theory’s influence on human physiology, such as heart rate variability, and the mathematical beauty of fractals. Additionally, the hosts explore philosophical viewpoints, emphasizing how accepting life’s uncertainties can foster adaptability and resilience.

In this episode of Breaking Math, we dive deep into the transformative power of large language models (LLMs) like GPT-4 in the fields of chemistry and materials science, based on the article "14 examples of how LLMs can transform materials science and chemistry: a reflection on a large language model hackathon" by Jablonka et al. from the Digital Discovery Journal. Discover how AI is revolutionizing scientific research with predictive modeling, lab automation, natural language interfaces, and data extraction from research papers. We explore how these models are streamlining workflows, accelerating discovery, and even reshaping education with personalized AI tutors.

In this episode of Breaking Math, we explore the unexpected link between sheep herding and fluid dynamics!  Did you know that the way sheep move in a herd is governed by the same mathematical principles as water flowing in a river? By following simple rules of alignment, cohesion, and separation, sheep create a coordinated, fluid-like movement that scientists can model to predict behavior.

In this exciting episode of Breaking Math, we explore the groundbreaking discovery of the largest prime number ever found—M136279841, a Mersenne prime with over 41 million digits! Join us as we dive deep into the story behind this astonishing mathematical achievement, led by Luke Durant, a volunteer from the Great Internet Mersenne Prime Search (GIMPS) project.

In this episode of Breaking Math, hosts Gabriel Hesch and Autumn Phaneuf dive into the cutting-edge world of Generative Flow Networks (GFlowNets) and their role in artificial intelligence and material science. The discussion centers on how GFlowNets are revolutionizing the discovery of new materials for carbon capture, offering a powerful alternative to traditional AI models. Learn about the mechanics of GFlowNets, their advantages, and the groundbreaking results in developing materials with enhanced CO2 absorption capabilities. The episode also explores the future potential of GFlowNets in AI-driven material discovery and beyond, emphasizing their transformative impact on carbon capture technology and sustainable innovation.

Explore the intriguing intersection of science and spiritualism in the Victorian era. This episode uncovers how prominent scientists like Michael Faraday, William James, and Marie & Pierre Curie engaged with supernatural phenomena and the rise of spiritualism. Discover the scientific efforts to debunk or understand paranormal activities, and how these investigations shaped modern science. Dive into the fascinating legacy of this 19th-century movement and its lasting impact on today's scientific inquiries into the unknown. Perfect for fans of history, science, and the supernatural.

AI & Consciousness: Philosophical Debates, Ethical Implications & the Future of Conscious Machines

In this episode of Breaking Math, hosts Autumn and Gabriel take a deep dive into the paper “Towards Equilibrium Molecular Conformation Generation with GFlowNets” by Volokova et al., published in the Digital Discovery Journal by the Royal Society of Chemistry. They explore the cutting-edge intersection of molecular conformations and machine learning, comparing traditional methods like molecular dynamics and cheminformatics with the innovative approach of Generative Flow Networks (GFlowNets) for molecular conformation generation.

Mathematical Patterns in Plants: Fibonacci, Golden Ratio & Nature's Hidden Math with Christophe Gole & Nancy Pick

Math & Cartography: Dr. Paula Rowinska on Map Projections, Gerrymandering & Real-World Math

In this conversation, Gabriel and Autumn interview Jeff Perry, a career coach and author of the book 'The Intentional Engineer'. They discuss the importance of being intentional in one's career, understanding one's passions and skills, and building a strong professional network. Jeff shares his journey from being an engineer to becoming an engineer coach and offers advice on how to navigate career transitions. They also explore the concept of 'genius zones' and how to identify and leverage one's unique strengths and talents. In this conversation, Jeff discusses the concept of the zone of incompetence, competence, excellence, and genius. They share personal anecdotes and examples to illustrate these zones and emphasize the importance of self-awareness and collaboration. They also touch on the role of mindset in driving behavior and results, particularly in the context of engineering and tech careers. Jeff offers coaching and resources for individuals looking to make intentional career shifts or upgrades.

Math & Language: Creativity, Quantification, and Making Math Accessible with Ben Orlin

In this episode Autumn and Dr. Jonathan Schwabish discuss the importance of strategic thinking in data visualization and the key elements of good data. He emphasizes the need to understand the data and how it was collected, as well as the importance of starting bar charts at zero. He also highlights common mistakes in data visualization, such as distorting or lying with visuals, and the potential impact of data visualization on policy decisions. Looking to the future, he discusses the role of AI in data visualization, the integration of AI into visualization tools, and the potential of augmented reality and virtual reality in data visualization. Jon Schwabish discusses the different data visualization tools he uses, including Excel, R, Tableau, Datawrapper, and Flourish. He emphasizes the importance of choosing the right tool for the specific use case and audience. He also highlights the need for policymakers and individuals to be trained in interpreting and using data visualizations effectively. Schwabish discusses the ethical considerations in data visualization, such as using inclusive language and considering accessibility.

In this episode, Gabriel and Autumn interview mathematician, comedian, and author Matt Parker about his latest book, "Love Triangle." They discuss the unique page numbering system in the book, which is based on the sine function, and how it adds an extra layer of discovery for readers. They also explore the use of triangles and quads in 3D modeling, the concept of Perlin noise, and the perception of randomness. The conversation touches on the intersection of mathematics and creativity, as well as the practical applications of mathematical concepts in various fields. The conversation explores various topics related to mathematics, including the analysis of the Mona Lisa, the use of math in playing pool, the discovery of new shapes, and the application of math in various fields. The speakers discuss the motivation behind exploring these topics and the interplay between math and art. They also provide advice for science and math content creators on YouTube.

Surprise! It's a Friday episode for you! Yes, yes it is a rerun, but we wanted to share it anyways.  We can't wait for our fall lineup because it's packed with surprises. See you back on Tuesday. 

It's the last week of our summer break and we have 2 episodes this week for you as a little treat. So check out our show on Friday too for a little bit more fun. We can't wait for our fall lineup because it's packed with surprises. If you have not listened to the last two episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered.

Happy Summer! We have another week of our summer break after this episode from 2018. We will be back shortly with more content and surprises!

Happy Summer! Check out part one of our three part series on black holes from 2018. Enjoy!

In this minisode, Autumn explores the basics in the world of journal rankings and metrics. She discusses the importance of journal rankings and how they are determined, focusing on metrics like impact factor, mathematical citation quotient (MCQ), and publication power approach (PPA). She explains how these metrics provide insights into a journal's influence and performance, but also emphasizes the need for a comprehensive evaluation of research beyond just metrics.

In this episode Autumn and Anil Ananthaswamy discuss the inspiration behind his book “Why Machines Learn” and the importance of understanding the math behind machine learning. He explains that the book aims to convey the beauty and essential concepts of machine learning through storytelling, history, sociology, and mathematics. Anil emphasizes the need for society to become gatekeepers of AI by understanding the mathematical basis of machine learning. He also explores the history of machine learning, including the development of neural networks, support vector machines, and kernel methods. Anil highlights the significance of the backpropagation algorithm and the universal approximation theorem in the resurgence of neural networks.

This discussion Autumn and Gabe delves into Ismar Volic's personal background and inspiration for writing the book, “Making Democracy Count” as well as the practical and theoretical aspects of voting systems. Additionally, the conversation explores the application of voting systems to everyday decision-making and the use of topological data analysis in understanding societal polarization. The conversation covers a wide range of topics, including data visualization, gerrymandering, electoral systems, and the intersection of mathematics and democracy. Volic, shares insights on the practical implications of implementing mathematical improvements in electoral systems and the legal and constitutional hurdles that may arise. He also discusses the importance of educating oneself about the quantitative underpinnings of democracy and the need for interdisciplinary discussions that bridge mathematics and politics.

In this conversation, Gabe and Autumn celebrate the 101st episode of Breaking Math and discuss the evolution of the podcast. They highlight the importance of creativity in teaching mathematics and share their plans to expand Breaking Math into Breaking Math Media. They also discuss the history of physics and the big questions that inform the podcast. The hosts express their desire to collaborate with listeners and explore practical applications of math in different fields. They also mention books like 'A Quantum Story' and 'Incomplete Nature' that delve into the mysteries of quantum mechanics and consciousness. The hosts highlight the unique and creative nature of their podcast, inviting listeners to join them in the Math Lounge, a metaphorical nightclub where math and creativity intersect.

In this episode of Breaking Math, Autumn and Gabe explore the concept of nothingness and its significance in various fields. They discuss the philosophical, scientific, mathematical, and literary aspects of nothingness, highlighting its role in understanding reality and existence. They mention books like 'Incomplete Nature' by Terence Deacon and 'Zero: The Biography of a Dangerous Idea' by Charles Seife, which delve into the concept of absence and zero. The episode concludes by emphasizing the complexity and versatility of nothingness, inviting listeners to think deeper about its implications.

In this conversation, Autumn Phaneuf interviews Zach Weinersmith, a cartoonist and writer, about the feasibility and implications of space settlement. They discuss the challenges and misconceptions surrounding space colonization, including the idea that it will make us rich, mitigate war, and make us wiser. They explore the potential of the moon and Mars as settlement options, as well as the concept of rotating space stations. They also touch on the physiological effects of space travel and the need for further research in areas such as reproduction and ecosystem design. The conversation explores the challenges and implications of human settlement in space. It discusses the lack of data on the long-term effects of space travel on the human body, particularly for women. The conversation also delves into the need for a closed-loop ecosystem for sustainable space settlement and the legal framework surrounding space exploration and resource extraction. The main takeaways include the importance of addressing reproductive and medical challenges, the need for a better legal regime, and the debunking of misconceptions about space settlement.

In this conversation, Autumn Phaneuf and Zach Weinersmith discusses his new book, A City on Mars, which takes a humorous look at the challenges of building a Martian society. He explores the misconceptions and myths surrounding space settlement and the feasibility of colonizing Mars. He argues that space is unlikely to make anyone rich and that the idea that space will mitigate war is unsupported. He also discusses the potential benefits and limitations of settling on the Moon and Mars, as well as the technical challenges involved.

Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.

Tom Chivers discusses his book 'Everything is Predictable: How Bayesian Statistics Explain Our World' and the applications of Bayesian statistics in various fields. He explains how Bayesian reasoning can be used to make predictions and evaluate the likelihood of hypotheses. Chivers also touches on the intersection of AI and ethics, particularly in relation to AI-generated art. The conversation explores the history of Bayes' theorem and its role in science, law, and medicine. Overall, the discussion highlights the power and implications of Bayesian statistics in understanding and navigating the world. 

Summary

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).  

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.  

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 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.  

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.

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?" 

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.

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. 

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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.

Transcripts of this episode are avialable upon request.  Email us at BreakingMathPodcast@gmail.com. 

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.

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.

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.

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!

Join Sofia Baca and her guests Millicent Oriana from Nerd Forensics and Arianna Lunarosa as they discuss energy.

An interview with Dr. Sabine Hossenfelder about her second book Existential Physics. Sabine is host of the famous youtube show Science with Sabine. 

The world around us is a four-dimensional world; there are three spatial dimensions, and one temporal dimension. Many of these objects emit an almost unfathomable number of photons. As we developed as creatures on this planet, we gathered the ability to sense the world around us; and given the amount of information represented as photons, it is no surprise that we developed an organ for sensing photons. But because of the amount of photons that are involved, and our relatively limited computational resources, it is necessary to develop shortcuts if we want to simulate an environment in silico. So what is raytracing? How is that different from what happens in games? And what does Ptolemy have to do with 3D graphics? All of this and more on this episode of Breaking Math.

Physical objects are everywhere, and they're all made out of molecules, and atoms. However, the arrangement and refinement of these atoms can be the difference between a computer and sand, or between a tree and paper. For a species as reliant on tool use, the ability to conceieve of, design, create, and produce these materials is an ongoing concern. Since we've been around as humans, and even before, we have been material scientists in some regard, searching for new materials to make things out of, including the tools we use to make things. So what is the difference between iron and steel? How do we think up new things to make things out of? And what are time crystals? All of this and more on this episode of Breaking Math.

Robert Black is an author who has written a six-book series about seven influential mathematicians, their lives, and their work. We interview him and his books, and take a peek into the lives of these influential mathematicians.

Seldom do we think about self-reference, but it is a huge part of the world we live in. Every time that we say 'myself', for instance, we are engaging in self-reference. Long ago, the Liar Paradox and the Golden Ratio were among the first formal examples of self-reference. Freedom to refer to the self has given us fruitful results in mathematics and technology. Recursion, for example, is used in algorithms such as PageRank, which is one of the primary algorithms in Google's search engine. Elements of self-reference can also be found in foundational shifts in the way we understand mathematics, and has propelled our understanding of mathematics forward. Forming modern set theory was only possible due to a paradox called Russel's paradox, for example. Even humor uses self-reference. Realizing this, can we find harmony in self-reference? Even in a podcast intro, are there elements of self-reference? Nobody knows, but I'd check if I were you. Catch all of this, and more, on this episode of Breaking Math. Episode 70.1: Episode Seventy Point One of Breaking Math Podcast

This episode description intentionally left blank!   As in completely on purpose.   Fun Fact!  The creators of the Breaking Math Podcast, Sofia and Gabriel always thought it was funny that many books that we've read - even going back to our childhood - had a page in it with the sentence printed, "This Page Intentionally Left Blank."   Like-  okay; what does this 'intentionally left blank page' add to the reading experience?  Does anyone know?  Oh look here!  There is a wikipedia page on it. Huh.  Now I know.  Now we know.   And knowing is half the battle!  

Michael Brooks is a science writer who specializes in making difficult concepts easier to grasp. In his latest book, Brooks goes through several mathematical concepts and discusses their motivation, history, and discovery. So how do stories make it easier to learn? What are some of the challenges associated with conveying difficult concepts to the general public? And who, historically, has been a mathematician? All of this and more on this episode of Breaking Math.  Songs were Breaking Math Intro and Outro by Elliot Smith of Albuquerque.  This episode is published under a Creative Commons 4.0 Attribute-ShareAlike-NonCommercial license. For more information, visit CreativeCommons.org  [Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Michael Brooks]

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.

The world is often uncertain, but it has only been in the last half millennium that we've found ways to interact mathematically with that concept. From its roots in death statistics, insurance, and gambling to modern Bayesian networks and machine learning, we've seen immense productivity in this field. Every way of looking at probability has something in common: the use of random variables. Random variables let us talk about events with uncertain outcomes in a concrete way. So what are random variables? How are they defined? And how do they interact? All of this, and more, on this episode of Breaking Math.

Join Sofía Baca with her guest Millicent Oriana from the newly launched Nerd Forensics podcast as they discuss some apparent paradoxes in probability and Russian roulette.

Katharine Hayhoe was the lead author on the 2018 US Climate Assessment report, and has spent her time since then spreading the word about climate change. She was always faced with the difficult task of convincing people who had stakes in things that would be affected by acknowledging the information in her report. In her newest book, “Saving Us: A Climate Scientist’s Case for Hope and Healing in a Divided World”, she discusses the challenges associated with these conversations, at both the micro and macro level. So who is Katherine Heyhoe? How has she learned to get people to acknowledge the reality of climate science? And is she the best, or worst, person to strike up a discussion about how the weather’s been? All of this, and more, on this episode of Breaking Math. Papers Cited: -“99.94 percent of papers agree with the scientific consensus.”

One tells a lie, the other the truth! Have fun with Sofía and Meryl as they investigate knight, knave, and spy problems!