# In Pursuit of the Unknown | Ian Stewart

Summary of: In Pursuit of the Unknown: 17 Equations That Changed the World

By: Ian Stewart

## Introduction

Embark on a journey through the world of mathematics with Ian Stewart’s book ‘In Pursuit of the Unknown: 17 Equations That Changed the World’. The provided summary covers the impact of equations like the Pythagorean theorem on mapmaking and measuring the shape of the universe, the development of topology driven by Euler’s formula, the importance of probability distribution in scientific research, and the revolutionary impact of the Navier-Stokes equation on modern transport. Delve into the nuances of Einstein’s theory of relativity, learn about Schrödinger’s equation in quantum theory, explore chaos theory’s applications in weather forecasting, and understand the Black-Scholes equation’s role in the financial sector’s growth and subsequent crisis in 2008-09.

## Measuring the Universe

The Pythagorean theorem’s simple equation allows us to calculate the sides and angles of any polygon, making it a vital first step in developing geometric techniques for making accurate maps. Though explicit triangulation is no longer used, technological advancements have allowed us to deduce locations from satellite data. Additionally, generalizations of Pythagoras’s theorem enable us to measure the shape and curvature of the universe. Triangles can be applied to spaces that are curved, allowing us to compute their curvature. Thus, by measuring triangles within space, we can attempt to measure the shape of the universe.

## Euler’s Formula and Its Impact on Mathematics

Euler’s formula, a simple but revolutionary statement in geometry, states that F-E+V=2, counting the numbers of faces, edges, and vertices in a polyhedron. This insight paved the way for a new kind of geometry, topology, which explores geometric shapes through the lens of bending and stretching. Topology distinguishes geometric objects by counting their faces, edges, and vertices, and it has applications in a wide range of fields, including biology. Mathematically analyzing the twists and turns of DNA allows for a better understanding of biological processes, such as how cells copy their DNA during cell division. Euler’s formula’s impact on mathematics continues to shape how we see and understand the physical world.

## The Bell Curve and Predictable Behaviors

In the 19th century, mathematicians discovered the normal distribution, also known as the bell curve. Although this was initially used in mathematics, the Belgian mathematician and sociologist, Adolphe Quetelet, extended this concept and applied it to social variables such as crime, births, deaths, height, weight, etc. The bell curve phenomenon indicated that people en masse behaved more predictably than individuals, which was unexpected since social variables’ underlying causes involved human choices and were believed to be too complex. The normal distribution is currently widely used in medical trials to test data reliability, thanks to a striking feature; the probability of errors in observational data follows this curve. By testing hypotheses such as the likelihood of a new drug being twice as efficient as an old one and whether this result occurred by chance, the reliability of the study can be established.

## The Power of the Navier-Stokes Equation

The Navier-Stokes equation is a mathematical formula that helps scientists predict the flow of fluids. This revolutionary equation has transformed modern transport, including ships, cars, and aircraft. Engineers often use computer solutions based on the equation for aerodynamic designs, which minimize resistance and ensure fuel efficiency. Additionally, medical researchers use the equation to calculate blood flow in the human body to aid surgeries like coronary bypass surgery. The equation even has applications in climate models to investigate climate change. With millions of cars, ships, and aircraft on the planet, the Navier-Stokes equation has drastically improved the reliability of fluid movement in modern transport. Its powerful influence can also be found in the medical and climate research fields.

## The Legacy of Newton’s Law of Gravitation

Newton’s law of gravitation revolutionized astronomy and space technology, enabling accurate predictions of the solar system’s motion. This law expresses the force of gravitational attraction between two bodies in terms of their mass and distance and asserts that gravitation acts universally. Newton’s law of gravitation still plays a vital role in designing spacecraft trajectories today. From Apollo missions to satellite communications, GPS, and interplanetary probes, it underpins a myriad of modern technologies. Although superseded by Einstein’s theory of relativity, Newton’s law of gravitation still reigns supreme for almost all practical purposes.