I have 0 knowledge about music and didn't have any access to music theory or any instruments in my life. What should be my pathway to have the basic ideas? I would love some good book recommendation about music theory. I would prefer books that assumes the reader has good mathematical background but lack any experience in music.
Decide which instrument you want to play and can afford, then understand that it doesn’t happen over night or over a fortnight and requires daily practice. We can not recommend books but I would say finding an instructor who is knowledgeable is 100 times better than a book I tried teaching myself with books and charts for 10 years and learned more in one year of music class than the previous 10 (Maybe I’m just slow). Even YouTube is a good resource.
Learning to read music is like learning to read anything else: you can’t start of reading Shakespeare and tongue twisters. Similarly, do not start out trying to learn your favorite Bach or Mozart piece. Everyone here will have different advice but don’t be discouraged by a lack of progress, it takes years to comprehend the world of music but once you do it is an amazing gift indeed.
There are many books about "music theory", but you're going to have a hard time reading them if you really "don't know anything about music". Now, the question is: do you really know nothing? My take is, you actually do know quite a bit. You know at least implicitly about rhythm and pitch, you can feel variations between instruments and so on. Mathematical background may be important but cannot really replace a good understanding of "what is going on" (at least based on my shallow studies on the matter).
I quote others, find an easy instrument (piano and guitar are nice to start with) to get the ropes of musical notation and accidents, and start from there. My music theory teacher suggested me to read the Dubois books as they are rather dry and "to the point", even if not accurate. If you manage to, it may be better to find some music theory teacher near you to get past the first milestones to avoid getting stuck. A decent number of websites (depending on your geographical location) may offer music graduates ready to teach you for a modest fee.
Always remember to pair theory with analytical listening, and possibly find someone more knowledgeable than you to double check ("I found this section of the 6th Symphony to be really uplifting but I don't know why: let's see what John thinks about it"). Taking a well-known masterpiece and analysing it over and over to discover more and more relations (and it's here that math starts to repay your work) will teach you at least as much as reading great books.
I would start with piano. There are tons of free apps or free "Online Piano"-websites. And piano combines so much of music! Another idea would be the drums to learn rhythm. Just listen to music you like and try to play along the basics like the bass drum and the snare.
You need a little bit of theory and praxis background, but there are tons of websites or videos on YouTube out there to understand these basics.
I don't know any good sources because I never searched for that. I just skipped through this video here and thought it's not that bad. Maybe a little to much to start with. Just use a picture of a keyboard while you watch the video. A picture like this: This image is from this video, wwhich would be a good start.: