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Why do mathematicians care about the Continuum Hypothesis? Does it have philosophical implications? If it was true or false, would it have had some sort of implications in mathematics?

Does the average mathematician ever need to care about this result?

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    $\begingroup$ I think that nowadays those who care about it are those who expect every statement to have a truth value. $\endgroup$ – Asaf Karagila Oct 8 '18 at 18:40
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    $\begingroup$ Your post would do better without the final question, which is entirely subjective. Pick your (least) favorite topic $X$ in any branch of mathematics and you can ask the same question: Does the average mathematician ever need to care about $X$? $\endgroup$ – Lee Mosher Oct 8 '18 at 18:45
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    $\begingroup$ @Lee: Since $X$ is one of the most used topological spaces, I imagine that the answer is yes. :P $\endgroup$ – Asaf Karagila Oct 8 '18 at 18:46
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    $\begingroup$ @user109871 What is an "average mathematician"? A mediocre one? if you mean "a typical one", then rather than saying that you need to explain what you mean, what sort of mathematicians you are trying to exclude in your description, and why you feel they need to be excluded (and why their exclusion is a meaningful thing to do). Part of what I mean is that if you intend to exclude people that actively think about blah, and then ask those that remain to say something insightful about blah, it is reasonable to find whatever is said suspect. $\endgroup$ – Andrés E. Caicedo Oct 8 '18 at 20:36
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    $\begingroup$ @Asaf We definitely need to get together for a drink or three. $\endgroup$ – Andrés E. Caicedo Oct 8 '18 at 23:00

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