>>14350533Because math is infinite. You can keep combining previous results to get new results. Some of those new results turn out to be mildly interesting. A typical 4-year degree should accomplish one main goal: get the student up to a competent level on analysis, algebra and topology. This is because those 3 fields deal with (mostly) separate mathematical structures that you need to understand if you even want to answer modern mathematical questions.
But that's it. Go to arxiv right now and find any paper tagged with analysis. You will see some friendly faces that you may know like integrals and limits but odds are that most of the terms used in the paper are unknown to you or at least would be unknown to someone with just a typical 4 year education. That's because mathematicians have kept pushing and kept making new objects to frame their questions better.
