If you know a little point-set topology, below is an unsolved math problem whose statement is relatively simple.
Probably everyone has at least seen the Mandelbrot set in some form, as it’s a popular object of mathematical artists. Here’s a picture from Wikipedia:
The formal definition is as follows. Let , where is a complex number. The Mandelbrot set is the complex plot of the set of complex numbers for which the sequence of iterates
remains bounded in absolute value.
We say is locally connected if every point admits a neighborhood basis consisting entirely of open, connected sets.
Conjecture: The Mandelbrot set is locally connected.