User blog comment:Primussupremus/Illogical numbers/@comment-29915175-20170415070717/@comment-5982810-20170421011236

In conclusion,

I believe  the only insight we can gain into the totality of mathematics is simply that it exists. Any actually useful form of mathematics can not encompass the totality of mathematics and must instead be a sub-set of it. It's these sub-sets where we can find useful and interesting results. Mathematics itself is absolutely infinite, we will never run out of things to study within it. At the same time, and perhaps as a consequence, we will never understand it completely as a whole.