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.

Takeaways

 * Networks are fundamental to understanding complex systems.
 * The COVID-19 pandemic highlighted the importance of network science.
 * Mathematics encompasses more than just numbers and shapes.
 * Personal experiences can lead to profound realizations about networks.
 * Everyday life is filled with examples of networks in action.
 * Game of Thrones and Survivor serve as engaging examples of network analysis.
 * The Bacon number illustrates connections in Hollywood.
 * Erdős number connects mathematicians through collaboration.

Chapters

 * 00:00 The Inspiration Behind the Book
 * 03:38 Understanding Networks: A New Perspective
 * 06:13 Networks in Everyday Life
 * 08:28 The Power of Networks in Society
 * 11:03 Real-World Applications of Network Science
 * 13:32 Pop Culture and Network Analysis
 * 15:38 The Bacon Number and Network Connections
 * 21:53 The Bacon Number and Small World Phenomenon
 * 26:34 Network Embeddings and Their Applications
 * 31:04 Graph Theory: Patterns and Connections
 * 35:11 The Importance of Mathematics in Everyday Life
 * 36:57 Introduction and Curiosity in Connections

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email: breakingmathpodcast@gmail.com

Dots and Lines: Hidden Networks

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.

Takeaways

 * Math is a powerful tool that can empower individuals.
 * The concept of Robin Hood Math aims to redistribute mathematical knowledge.
 * Mathematical literacy is becoming as essential as reading.
 * Algorithms are deeply embedded in our daily lives, influencing decisions.
 * Understanding expected value can improve decision-making.
 * Averaging guesses can lead to better predictions.
 * Social media algorithms prioritize engagement, affecting content visibility.
 * Credit scores are calculated using weighted sums of various factors.
 * Many important mathematical concepts are simpler than they appear.
 * Mathematical literacy can help close equity gaps in society.

Chapters

 * 00:00 Monetizing Social Media for Educators
 * 02:25 The Birth of Robin Hood Math
 * 05:18 Empowering the Everyday Person with Math
 * 08:01 The Writing Process and Surprising Discoveries
 * 10:37 Practical Math Lessons for Everyday Life
 * 13:22 Understanding Algorithms in Social Media
 * 21:56 Understanding Engagement Algorithms
 * 24:28 The Impact of Mathematics on Financial Decisions
 * 29:54 Empowering Through Mathematical Literacy
 * 32:23 Exploring Key Themes in Mathematics

Follow Noah on Twitter [https://x.com/ProfNoahGian], BlueSky [https://bsky.app/profile/profnoahgian.bsky.social], Instagram [https://www.instagram.com/profnoahgian/], LinkedIn [https://www.linkedin.com/in/noah-giansiracusa-a316a4315/] and on his Website [https://www.noahgian.com/]
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email: breakingmathpodcast@gmail.com

Robin Hood Math

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.

Takeaways

 * Programming languages can optimize swim training.
 * There's a gap in literature between math and sports science.
 * Data exchange in swimming training is challenging.
 * Visualizing swimming techniques aids in understanding.
 * Mathematical patterns can enhance training routines.
 * Repetitive tasks in swimming can be likened to repetitive songs.
 * Engagement in training is crucial for success.
 * 

Chapters

 * 00:00 The Motivation Behind Swim Training Patterns
 * 02:32 Intersection of Swimming and Computer Science
 * 05:56 Challenges in Measuring and Documenting Swim Performance
 * 09:32 The Role of Patterns in Swim Training
 * 11:54 Mathematical Patterns and Their Application in Swimming
 * 15:14 Exploring Repetitiveness in Music and Swim Training
 * 18:08 Art Projects and Mathematical Patterns
 * 21:13 Fermat's Theorem and Impossible Squares
 * 23:14 Making Math Accessible in Swim Training
 * 26:40 The Importance of a Shared Language in Coaching
 * 27:35 Applying Pattern-Based Approaches to Sports
 * 29:17 The Role of Structure in Training Across Sports
 * 30:02 Current Use of Frameworks in Elite Swimming
 * 30:10 Innovative Training Philosophies in Swimming
 * 32:30 Programming Languages and Their Applications in Sports Science
 * 34:56 The Joy of Writing and Creating
 * 38:59 Challenges in Writing and Communicating Mathematical Concepts
 * 41:37 The Journey of a Book and Community Engagement

Follow Christoph on his YouTube Channel and on bartneck.de.
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email: breakingmathpodcast@gmail.com

What are Swim Training Patterns?

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.

Takeaways

 * AI systems can misinterpret student behavior, leading to false accusations.
 * Bias in AI reflects historical prejudices encoded in data.
 * Predictive analytics can help identify at-risk students but may alter their outcomes.
 * Anonymization of data is often ineffective in protecting privacy.
 * Differential privacy offers a way to share data while safeguarding individual identities.
 * Ethics should be a core component of algorithm design.
 * The impact of biased algorithms can accumulate over time.
 * Mathematicians must understand both technical and human aspects of AI.
 * Society must question the values embedded in AI systems.
 * Small changes in initial conditions can lead to vastly different outcomes.

Chapters

 * 00:00 Introduction to AI Ethics
 * 02:14 The Accuracy and Implications of AI in Education
 * 04:14 Bias in AI and Its Consequences
 * 05:45 Data Privacy Challenges in AI
 * 06:37 Mathematical Solutions for Ethical AI
 * 08:04 The Role of Mathematicians in AI Ethics
 * 09:42 The Future of AI and Ethical Considerations

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email: breakingmathpodcast@gmail.com





AI Ethics: Algorithms Go To College

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.

Takeaways

 * The shuffle feature is not truly random.
 * Humans struggle to recognize true randomness due to cognitive biases.
 * The Fisher-Yates shuffle algorithm is a standard for randomization.
 * Uses psychological techniques to enhance user satisfaction with shuffle.
 * Dithering is a method used to create a perception of randomness.
 * Shuffle feature analyzes multiple dimensions to optimize song selection.
 * The algorithm incorporates noise to maintain unpredictability.
 * Curated randomness is prevalent in various technologies beyond music.
 * Humans prefer sequences with fewer clusters to feel more random.
 * Mathematics can reveal insights into human behavior and preferences.

Chapters

00:00 The Hidden Mathematics of Spotify Shuffle

05:56 The Art of Psychological Randomness

07:58 Philosophical Implications of Curated Randomness

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email: breakingmathpodcast@gmail.com



Random Shuffle Isn't Random At All

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.

Takeaways:

 * Mathematics powers seemingly magical technologies like AI.
 * Algorithms are sets of instructions that guide AI processes.
 * Machine learning finds patterns in data through trial and error.
 * Linear algebra organizes data into vectors and matrices.
 * Calculus helps AI find optimal solutions to problems.
 * Probability theory allows AI to express uncertainty in predictions.
 * AI applications include medical diagnostics and financial algorithms.
 * Self-driving cars use mathematics to navigate and make decisions.
 * Mathematical literacy is crucial in an AI-driven world.
 * Understanding AI's math gives individuals agency in technology.



Chapters: 

00:00 The Mathematical Heart of AI

03:28 Mathematics in Action: Real-World Applications

05:33 Empowerment Through Understanding Mathematics

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Algorithms & AI Simplified - The Not So Mathy Version

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.

All opinions are of the individual scientist and do not reflect the opinions of NIST or the federal Government.

Takeaways

 * Quantum computers harness principles of quantum physics for computation.
 * Shor's algorithm can efficiently factor large numbers, threatening RSA encryption.
 * Post-quantum cryptography aims to develop algorithms resistant to quantum attacks.
 * NIST is leading the effort to standardize post-quantum cryptographic algorithms.
 * Lattice-based algorithms are promising for post-quantum cryptography due to their efficiency.
 * Businesses must be proactive in transitioning to post-quantum cryptography.
 * The Harvest Now, Decrypt Later threat highlights the urgency of transitioning.
 * Quantum key distribution offers theoretically perfect security.
 * Different cryptographic algorithms are needed for various applications and devices.
 * The future of cryptography will rely on new mathematical challenges to ensure security.

Keywords

quantum computing, cryptography, post-quantum cryptography, NIST, cybersecurity, Shor's algorithm, digital signatures, lattice-based algorithms, encryption, quantum threats

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What is Cryptography?

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.

All opinions are of the individual scientist and do not reflect the opinions of NIST or the federal Government.

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We Live in a Radioactive World: What is Dosimetry?

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.

All opinions are of the individual scientist and do not reflect the opinions of NIST or the federal Government.

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What is Life?

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.

You can learn more about Time at time.gov and NIST at nist.gov.

All opinions are of the individual scientist and do not reflect the opinions of  NIST or the federal Government.

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email: breakingmathpodcast@gmail.com

Fire Science: What are Photoacoustic Measurements?

Breaking Math is a deep-dive science, technology, engineering, AI, and mathematics podcast that explores the world through the lens of logic, patterns, and critical thinking. Hosted by Autumn Phaneuf, an expert in industrial engineering, operations research and applied mathematics, and Gabriel Hesch, an electrical engineer (host from 2016-2024) with a passion for mathematical clarity, the show is dedicated to uncovering the mathematical structures behind science, engineering, technology, and the systems that shape our future.

What began as a conversation about math as a pure and elegant discipline has evolved into a platform for bold, interdisciplinary dialogue. Each episode of Breaking Math takes listeners on an intellectual journey—whether it’s into the strange beauty of chaos theory, the ethical dilemmas of AI, the deep structures of biological evolution, or the thermodynamics of black holes. Along the way, Autumn and Gabriel interview leading thinkers and working scientists from across the spectrum: computer scientists, quantum physicists, chemists, philosophers, neuroscientists, and more.

But this isn’t just a podcast about equations—it’s a show about how mathematics influences the way we think, create, build, and understand. Breaking Math pushes back against the idea that STEM belongs behind a paywall or an academic podium. It’s for the curious, the critical, the creative—for anyone who believes that ideas should be rigorous, accessible, and infused with wonder.

If you've ever wondered:

 * What’s the math behind machine learning?
 * How do we quantify uncertainty in climate models?
 * Can consciousness be described in AI?
 * Why does beauty matter in an equation?

Then you’re in the right place.

At its heart, Breaking Math is about building bridges—between disciplines, between experts and the public, and between the abstract world of mathematics and the messy, magnificent reality we live in. With humor, clarity, and deep respect for complexity, Autumn and Gabriel invite you to rethink what math can be—and how it can help us shape a better future.

Listen wherever you get your podcasts.
Website: https://breakingmath.io [https://breakingmath.io/]
Linktree: https://linktr.ee/breakingmathmedia
Email: breakingmathpodcast@gmail.com

Breaking Math Podcast

Breaking Math's Show

A math podcast that explores science, creativity, and other faucets of the human experience numbers, axioms, and models.  BreakingMath.io [http://breakingmath.io/]

Breaking Math

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