Intersecting Us

Mathematics is often seen as the domain of certainty. Once something is proven, it feels settled. But every proof begins with assumptions. In this reflection, Dave explores one of the most surprising moments in mathematical history: the introduction of a number whose square is negative. At first it seemed impossible. Yet allowing that single assumption opened the door to the complex numbers — a ri...

For centuries, Euclid’s geometry seemed complete — a perfect system built from simple assumptions. But one assumption always stood out: the parallel postulate. Mathematicians struggled with it for generations. Some quietly explored what would happen if that assumption changed. When Bernhard Riemann finally asked the question openly, something surprising happened. Entirely new geometries appeared —...

For centuries, Euclid’s geometry seemed complete — a perfect system built from simple assumptions. But one assumption always stood out: the parallel postulate. Mathematicians struggled with it for generations. Some quietly explored what would happen if that assumption changed. When Bernhard Riemann finally asked the question openly, something surprising happened. Entirely new geometries appeared —...

Episode 3: The Actuary’s Leap Actuaries spend their careers studying risk. Using data, mortality tables, and probability, they calculate what is likely to happen across large populations. This work is built on a mathematical idea called expected value —the attempt to price the future based on what happens on average. But there is a limit to what the math can tell us. Even the best models can’t pre...

Episode 2: The Psychological Mirage Why do we crave certainty so deeply? In mathematics, a proof often ends with Q.E.D. — “that which was to be demonstrated.” It’s the satisfying period at the end of the argument. Solid ground. Finality. But in life, that kind of certainty is rare. Our minds naturally long for the feeling of complete safety — certainty about our health, our investments, our relati...

How certain do you need to be before you act? In this opening episode of Reasonable Hope , Brian reflects on a lesson from actuarial science: life rarely operates in absolutes. While mathematics often deals in certainty—0 or 1—our daily decisions live somewhere in between. Drawing from his years as an actuary, Brian explores the difference between certainty and confidence . Certainty is a psycholo...

In this episode, the discussion revolves around the theme of love and its many facets, from tough love to unconditional support. The conversation highlights the importance of intrinsic worth and identity beyond achievements, particularly in the context of mathematics and education. Personal stories and experiences underscore the transformative power of focusing on others, emphasizing the value of...

In this podcast episode, the hosts delve into the deep connections between mathematics, community, and personal growth. They discuss how struggling with mathematical proofs, like those of the Pythagorean Theorem, leads to a greater understanding and appreciation of their underlying principles. The conversation highlights the role of community and collaboration in overcoming these challenges and ma...

In this episode, the podcast delves into the multifaceted concept of freedom within mathematics, exploring its implications for exploration, imagination, understanding, and inclusion. Through examples like the Pythagorean theorem, Euler's contributions to topology, and the universal relevance of mathematical concepts like pi and E, the conversation highlights how mathematics transcends cultural an...

In this podcast episode, the hosts discuss the intersection of mathematics and justice, inspired by the ideas presented in a book. They delve into the concepts of primary justice, rectifying justice, and the importance of treating everyone with dignity and care. The conversation explores implicit biases, belonging, and the role of community in advocating for justice.

In this episode, the podcast delves into the transformative power of math, exploring how it can empower individuals, transcend physical limitations, and foster creativity and understanding. Through anecdotes like Chris's journey of mathematical discovery in prison and the proof of Fermat's Last Theorem, the discussion highlights how math can be a tool for personal growth and societal betterment. T...

In this podcast episode, the hosts discuss the concept of struggle and its role in personal growth and mastery, drawing from examples in mathematics and programming. They share stories of grappling with complex problems, finding unexpected insights, and the satisfaction of mastering difficult tasks. The conversation explores the difference between external and internal goods, emphasizing the value...

In this episode, the hosts explore the concept of truth and its pursuit, emphasizing the virtues of intellectual humility, admitting mistakes, and avoiding overgeneralizations. They discuss how mathematics aids in understanding truth, from correcting errors in data to defining new concepts like imaginary numbers. The hosts encourage listeners to embrace the journey of seeking truth, acknowledging...

In this podcast episode, the hosts discuss the concept of permanence, focusing on the Pythagorean Theorem as an eternal and underappreciated equation. They explore the beauty and truth embedded in the theorem and its various proofs throughout history, emphasizing its role as a reliable foothold in the world of mathematics. The hosts connect the permanence of mathematical truths to the broader them...

In this podcast passage, the hosts discuss the multifaceted nature of beauty in mathematics, exploring sensory, wondrous, insightful, and transcendent dimensions. They delve into the aesthetic aspects of mathematical patterns, the elegance of proofs, and the pursuit of deeper understanding. The concept of transcendent beauty is highlighted, drawing parallels with transcendental numbers like Pi and...

The passage discusses various ways to celebrate Pi Day, including enjoying pie, making pie jokes, or simply acknowledging the significance of pi. It emphasizes that Pi Day should be about trying new things, as pi itself represents a unique concept beyond just being a number. The conversation delves into the deeper meaning of pi as a relationship between the circumference and diameter of a circle,...

The podcast discusses the intersection of work and play in mathematics, emphasizing the value of community and collaboration in learning. It explores the evolving landscape of math education, encouraging a shift towards discovery, play, and freedom in the learning process. The hosts share personal experiences with exams, teamwork, and the joy of teaching, highlighting the importance of perseveranc...

In this podcast episode, the hosts delve into the intrinsic meaning and value found in mathematics. They discuss the existential aspect of math, emphasizing the importance of understanding the underlying significance of mathematical concepts rather than merely memorizing steps. The hosts explore the history of mathematicians and the joy of connecting with their journeys, appreciating the permanenc...

Summary: In this podcast episode, the hosts discuss decision-making, free will, and philosophical concepts. They delve into personal experiences, neuroscience, and the intersection of determinism and free will. Later, the conversation shifts to mathematicians Descartes and Fermat, exploring their contrasting lives and contributions, emphasizing Fermat's last theorem.

In this podcast episode, the hosts engage with two guests, Charlie and Prabal, discussing their experiences in the actuarial field, decision-making, and the application of actuarial skills in personal business ventures. Charlie shares insights on using risk analytics tools from his actuarial training in his investment strategies, emphasizing concepts like risk pricing, asset and liability manageme...

In this podcast episode, the hosts discuss the concept of mathematical exploration, drawing parallels to Steve Jobs' approach to technology by emphasizing understanding over mere memorization. They delve into the fascinating world of irrational numbers, particularly focusing on the square root of two and its infinite, non-repeating decimals. The hosts also share personal experiences with mathemati...

In this podcast episode, the hosts delve into the first chapter of "Mathematics for Human Flourishing" by Francis Su, exploring the philosophical and transformative aspects of math in one's life. They discuss Simone Weil's quote, the story of Christopher Jackson, and the profound connections between mathematics, virtue, and human flourishing.

In this podcast episode, Alec, an actuarial analyst, shares insights about his journey through exams, career, and personal growth. He emphasizes the importance of studying efficiently and cultivating a growth mindset. The discussion delves into the significance of setting meaningful goals, evolving them as needed, and finding passion in one's pursuits. Alec reflects on the impact of the book "Math...

In this podcast, the hosts explore the boundary between real and artificial intelligence, questioning whether AI possesses genuine sentience and emotions. They delve into the implications of humans forming relationships with AI and discuss the ethical dilemmas surrounding these interactions. Referencing historical figures, they emphasize the importance of community discussion in navigating the imp...

In these passages, the podcast explores Euler's Identity, a remarkable mathematical formula that combines the constants e , π , and i, in a seemingly improbable way: Despite their disparate origins, these constants harmonize beautifully in this concise equation. The discussion highlights the real-world applications of Euler's Identity in fields such as physics, music theory, and wave studies. The...