Introduction: The Beauty of Mathematics

Unsolved Mathematical Mysteries

In this course, Professor Satyan Devadoss (University of San Diego) explores some of the most fascinating unsolved problems in mathematics. In the first mini-lecture, we discuss reasons why we should care about cutting-edge mathematics, emphasising the beauty of such mathematics over its usefulness. In the second mini-lecture, we learn about the infinite list of prime numbers and consider the unsolved problem of whether there are infinitely many twin primes. In the third mini-lecture, we look at an unsolved problem called the Happy Ending Problem, that involves drawing simple objects such as dots, lines, and polygons. In the fourth mini-lecture, we look at an unsolved problem in mathematics that involves tying knots. In the fifth mini-lecture, we think about an unsolved problem involving the side and diagonal lengths of boxes, as well as how to draw three-dimensional boxes on a flat plane.

Introduction: The Beauty of Mathematics

In this mini-lecture, we discuss why we should care about mathematics and think about what cutting-edge mathematics involves. In particular, we consider: (i) cutting-edge problems in other disciplines including biology, chemistry, physics, economics, art, and music; (ii) the beauty of mathematics; (iii) how the more maths you know the more questions there are to consider; and (iv) how even with a basic understanding of maths, you can access a whole world of beautiful, cutting-edge, unsolved problems in mathematics.