Do you think that math and humanities are two divergent interests

or is it false dichotomy to say that is usually "either/or" for most people?

Math is the logical expression of our abstract, sometimes subconscious minds. People that are generally gifted in math (at the level of competing in math contests) are fairly quick problem solvers and have very high IQs. They are usually poor to about average in linguistic abilities and are sometimes handicapped in the writing and reading comprehension departments compared to the average person.

Humanities encompasses all of the language-based liberal arts. People study the ways to articulate their flow of thoughts so that it has precise clarity to the audience that they are talking to. Literary types also happen to have strong writing skills. They can write at the university level for any kind of expository paper - be it historical, personal or philosophical. The only handicap is that these people's choice of study prohibits them to gauge their thoughts at a deeper, more rigorous abstract level, thus the reason why some call these subjects the "soft sciences." In reality though, the ability to articulate displays a clarity of thought, even if those underlying assumptions used may be faulty. There is still that display of thinking which requires stimulation.

To put more sharply: we (technical degree holders) can do what they do, but they cannot do what we do. You would have to go to school to be able to understand and work in our fields. Liberal arts education certainly is best learned in a university setting, but any layperson can also pursue their own education in this discipline. It is not complicated. How hard can your native language really be to use, and further how hard can ideas in history, even philosophy really be? Especially fields like philosophy, though it may be tasking, it is not completely inaccessible on your own.

Science consists of analytical disciplines where phenomena in the universe may be objectively observed, understood, and predicted and/or replicated. Some fields in humanities are labeled with aid of the word "science," but most anyone you ask in a physical science will not agree there is anything science-relevant about it. It is not about being hoggish with the word or anything trivial, many of us just do not agree with the extension of this definition. Even fields like psychology, or behavioral science are not "sciences." There is a difference between taxonomy and science, and the former is often more appropriate in your aforementioned soft sciences.