User blog comment:Holomanga/Learn all of Maths I: Algebra and Functions/@comment-24.34.11.217-20151101164432/@comment-39162-20151102231146

Not me personally (I'm nowhere near smart enough to do that, since all the low-hanging fruit were taken centuries ago, and don't plan on studying anything that would give me the skills to do it), but if you just mean the abstract you then hypothetical people can make their own fields of maths.

Generally, these will be subfields of extant fields - the study of Tits buildings is part of the study of Lie groups, which is itself part of Group theory which is part of the broad field of abstract algebra.

Whether a new mathematical idea one has becomes a new field really depends on how many mathematicians pick it up and start proving theorems about it: if other people like the newly defined structures for whatever reason, they may develop into a field themselves.

Not to say that there aren't some low hanging fruit around that have just been unclaimed - Googology is an example of an essentially new field of maths that only really started being developed this century. Nonetheless, it would take a huge amount of ingenuity to recognise any potential "easy" field as one, and I doubt there are many left.