Why are there so few Euclidean geometry problems that remain unsolved?

math-history soft-question euclidean-geometry

Solution 1:

Because Euclidean geometry is currently not fashionable, most people do not study topics in it or discuss problems in it, and so you simply hear of fewer problems, solved or unsolved.

Any claims that all Euclidean geometry problems are decidable, as given in the comments to the question, will depend on some restricted definition regarding the form that a "problem" can take.

There are plenty of unsolved geometry problems. I recommend the book Unsolved Problems in Geometry by Croft, Falconer, & Guy (1991). In addition to hundreds of problems, the book even points to 17 other collections of unsolved geometry problems.

Many of these unsolved problems are fairly easy to state. For example: Among all configurations of $n$ points not all on one line, what is the minimum number of lines they might determine? Explainable to a small child, yet unsolved.

There are many, many beautiful unsolved geometry problems, including ones with Erdös rewards, and I cannot do them justice in this answer.

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