There are about 100 big research areas in mathematics, each of which is subdivided into several dozen smaller areas: see the AMS subject classification here. So it is fair to say that there are several thousand research directions within mathematics. Within these, mathematicians publish more than 100 thousand papers each year.

There are many big problems on which mathematicians agree. For these, I recommend you to read the Notices of the AMS and the Bulletin of the AMS. You can also start your exploration here.

Finally, note that this site is for research mathematicians (who already know the answer to your question).