Mathematicians make progress on coloring

One of the most famous coloring problems concerns the "chromatic number of the plane." What does that mean? The aim is to assign a color to every point in the plane so that any two points one unit apart always have different colors. The object of the game, of course, is to use as few colors as possible. This minimum number is called the chromatic number of the plane, denoted χ (ℝ²).

A simple equilateral triangle is enough to show that χ (ℝ²) ≥ 3. In 1961, Canadian mathematician Leo Moser (1921–1970) proposed a graph, sometimes called the Moser spindle or spindle graph, which shows that χ (ℝ²) ≥ 4. It was soon established that χ (ℝ²) ≤ 7, but the bounds were not improved until 2018; the question remains open today (see box).

With just one color! --------------------