How do I say that I am interested in a lot of things without coming off either as superficial or arrogant
Try jack of all trades. It means you're good at many things and have a variety of skills.
A word would be versatile.
Addition - If the above two options don't work for you, try a fancy word that would make you sound smart and good at english, just the way you want them to think of you, good at many things, a protean.
Quite avoiding terms like Renaissance Man I'd suggest versatile.
2: embracing a variety of subjects, fields, or skills; also : turning with ease from one thing to another
Reference:
http://www.merriam-webster.com/dictionary/versatile
Keeping it simple: "I have a wide range of interests, including...".
But be forewarned, each of your example subjects can be broken up into smaller subjects, some of which you may actually dislike! The more you learn, the more you discover how little you really know!
Most of the replies here imply a level of skill. Being interested at something doesn't necessarily mean being good at it.
If you're simply looking tor something that means interest in subjects, here are some suggestions:
- eclectic tastes
- varied interests
- diverse hobbies
- engrossed in many subjects
- a kaleidoscope of topics
(feel free to pick & mix)
Polymath could work:
I'm a bit of a polymath: I like maths but also love history and am pretty good at sports.
This fits the "not arrogant" part as long as you say it in a self-deprecating way, perhaps with a smile and a slightly sardonic tone.
From Wikipedia:
A polymath is a person whose expertise spans a significant number of different subject areas; such a person is known to draw on complex bodies of knowledge to solve specific problems. The term was first used in the 17th century; the related term, polyhistor, is an ancient term with similar meaning.