Let’s take a moment to get our hands on some sets of numbers and the arithmetic progressions those sets contain, starting with the prime numbers, perennial favorites of math enthusiasts.

To determine the next number in the sequence, you simply sum together the previous two numbers. You can repeat this process to generate an infinitely long Fibonacci sequence.

The Fibonacci Sequence Is Everywhere—Even the Troubled Stock Market The curious set of numbers shows up in nature and also in human activities.

The Fibonacci sequence has many interesting properties. One is that fractions formed by successive Fibonacci numbers—e.g., 3/2 and 5/3 and 8/5—get closer and closer to a particular value ...

For example, in the question on the former slide, there are five numbers between each number in the sequence. That means that the final number would be 20 + 5, or 25.

The Game of Trees is a Mad Math Theory That Is Impossible to Prove Just writing the proof would take longer than the theoretical age of the universe.

Others are so common that they seem impossible to avoid. A new proof by Sarah Peluse of the University of Oxford establishes that one particularly important type of numerical sequence is, ultimately, ...