Take an outline map of the lower 48 U.S. states and four crayons. Can you shade in the map so that every state is a different color than each of its neighbors, without resorting to a fifth color? This ...

Imagine you're a mapmaker, ready to finish your masterpiece map of the world. The only thing left to do is add the colors. But how many colors do you need for the countries if you want to make sure no ...

IIIF provides researchers rich metadata and media viewing options for comparison of works across cultural heritage collections. Visit the IIIF page to learn more. This computer printout relates to the ...

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...

2025’s most surprising breakthroughs in biology included a finding that a father’s environmental exposures can impact the development of their offspring, research confirming that intelligence evolved ...

Kenneth Appel, 80, who successfully brought the computer to bear on a celebrated mathematical problem that, in its capacity to perplex, tantalize and frustrate, conformed to a common view of ...

Computers can be valuable tools for helping mathematicians solve problems but they can also play their own part in the discovery and proof of mathematical theorems. Perhaps the first major result by a ...