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In Pursuit of the Unknown

Ian Stewart

Duration26 min
Key Points9 Key Points
Rating4.5 Rate

What's inside?

Explore the power and influence of 17 groundbreaking equations that have shaped history and continue to impact our daily lives.

You'll learn

Learn1. The backstory and impact of 17 big math equations
Learn2. How these equations show up in daily life
Learn3. The basics of math and physics
Learn4. How to see the beauty in math
Learn5. How these equations shaped tech and society
Learn6. The tales of the brains behind these equations.

Key points

01The Dawn of Mathematics: Pythagoras' Theorem

The birth of Pythagoras around 570 BC on the island of Samos marked the beginning of a journey that would forever change the world of mathematics and beyond. As a philosopher and mathematician, Pythagoras is best remembered for his groundbreaking theorem, a cornerstone of Euclidean geometry. This theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, was a significant leap forward in mathematical understanding. Pythagoras' early years were marked by extensive travels, particularly to Egypt and Babylon. These journeys were not merely geographical but intellectual, as he absorbed mathematical concepts that would later form the bedrock of his theorem. Upon his return to Samos, he established a philosophical and religious school, a hub for the dissemination of his mathematical and philosophical ideas. The influence of the Pythagorean theorem is far-reaching, permeating various fields of study and practical applications. In architecture, it is a vital tool for ensuring that structures are built with right angles, contributing to their structural integrity. Engineers rely on it for the design and construction of bridges, buildings, and other structures. It also finds application in navigation, physics, computer science, and numerous other fields, underscoring its universal relevance. The construction of the Great Pyramid of Giza in Egypt serves as a testament to the practical utility of Pythagoras' theorem. The builders of this ancient wonder used the theorem to ensure that the pyramid was built with precise right angles, a feat that would have been impossible without this mathematical principle. Beyond the theorem, Pythagoras' influence extended to the establishment of the Pythagorean school in Croton, a city in southern Italy. This institution was more than a place of learning; it was a community where members lived and worked together, adhering to the Pythagorean way of life. The school played a pivotal role in propagating Pythagoras' teachings, and its influence is still palpable in modern mathematics and philosophy. In essence, the impact of Pythagoras' theorem on the world is profound, shaping our understanding and interaction with the world around us. It is a testament to the power of mathematics, a language that transcends cultural and temporal boundaries, and continues to illuminate our path as we navigate the complexities of the universe.

02The Power of Numbers: Logarithms

In the early 17th century, a revolutionary mathematical concept was introduced by Scottish mathematician John Napier. This concept, known as logarithms, forever changed the landscape of mathematics and its application in various fields. The invention of logarithms was a significant milestone that simplified complex calculations, reducing the time and effort required for computations, particularly multiplication and division of large numbers. The impact of Napier's invention was far-reaching, extending beyond the realm of mathematics. In the field of astronomy, the use of logarithms brought about a significant advancement. It made it easier for astronomers to calculate distances between celestial bodies and their movements. This development allowed for more accurate predictions and observations, contributing to our understanding of the universe. The cosmos, once a vast and mysterious expanse, became more comprehensible thanks to the power of logarithms. In the Age of Exploration, accurate navigation was paramount to discovering new lands and sea routes. Here, too, logarithms played a crucial role. They were instrumental in the development of accurate sea charts, enabling navigators to calculate longitudes more precisely. This led to safer and more efficient sea voyages, underscoring the importance of logarithms in the progress of exploration and navigation. The influence of logarithms also extended to the world of finance. They revolutionized the way interest calculations were made, making the concept of compound interest, which is fundamental to finance, easier to understand and calculate. This led to more accurate financial forecasting and planning, contributing to the development of modern financial systems. The complexities of finance were made more manageable, thanks to the transformative power of logarithms. Moreover, Napier's invention paved the way for the development of slide rules, a mechanical analog computer. Based on logarithmic scales, the slide rule was a practical tool that made complex calculations manageable. It was widely used for calculations until the mid-20th century in various fields, including engineering and aviation. The slide rule, a testament to the practical application of logarithms, was an indispensable tool for many professionals. In conclusion, the invention of logarithms by John Napier was a groundbreaking development that had a transformative impact on various fields. From astronomy to navigation, and finance, the power of logarithms has been instrumental in simplifying complex calculations and advancing our understanding of the world. The power of numbers, as embodied by logarithms, continues to shape our world, underscoring the enduring legacy of Napier's invention.

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03The Language of the Universe: Newton's Law of Gravity

04The Heart of Matter: The Law of Conservation of Energy

05The Fabric of Reality: Einstein's Theory of Relativity

06The Code of Life: The Equation of Life

07The Edge of Chaos: The Logistic Map

08The Future of Computation: Turing's Theory of Computation

09Conclusion

About Ian Stewart

Ian Stewart is a British mathematician and popular-science and science-fiction writer. He is Emeritus Professor of Mathematics at the University of Warwick, England, and is known for his work on catastrophe theory and symmetry.

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