experimental mathematics four-color theorem Kepler conjecture sphere packing experimentation or conjecture proven computing prove
In return, computing has also become essential for obtaining new results. This is a group of techniques known as experimental mathematics, which is the use of experimentation to discover mathematical insights. The most well-known example is the four-color theorem, which was proven in 1976 with the help of a computer. This revolutionized traditional mathematics, where the rule was that the mathematician should verify each part of the proof. In 1998, the Kepler conjecture on sphere packing seemed to also be partially proven by computer. An international team had since worked on writing a formal proof; it was finished (and verified) in 2015.
