Over the centuries, mathematicians have developed a variety of methods of solving equations. Using the capabilities of modern computers, they have explored in detail how these age-old recipes work–when the methods can be relied upon, when they fail, and when they behave strangely.
![](https://i0.wp.com/www.sciencenews.org/wp-content/uploads/2003/04/2804.gif?resize=150%2C150&ssl=1)
![](https://i0.wp.com/www.sciencenews.org/wp-content/uploads/2003/04/2805.gif?resize=150%2C150&ssl=1)
![](https://i0.wp.com/www.sciencenews.org/wp-content/uploads/2003/04/2806.gif?resize=150%2C150&ssl=1)
![](https://i0.wp.com/www.sciencenews.org/wp-content/uploads/2003/04/2807.gif?resize=150%2C150&ssl=1)
Such computer explorations have also yielded vivid visual representations of the underlying mathematical processes. At the same time, a few artists have taken advantage of the techniques used to visualize mathematics to create aesthetically pleasing patterns and intriguing artworks.