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 ...

URBANA — Here's the task: Color a map of the United States so that no two adjacent states have the same color. What's the least amount of colors you would need? The answer to that question took ...

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 ...