I have often seen mathematics and symbolic codes that I cant read. I have seen books with writing but I find in lucid dreams I am dyslexic and the letters wont stay still so reading is a challenge. I have heard music, usually sounding late classical orchestral, but not music I know and since I have no skill I cant record with musical notation. I have found to my surprise that I can write down my name, address, phone number and have asked entities to contact me if they are able to do so. So far no one has. I do simple arithmetic in my dream head but since the capacity to externalize in any medium is difficult it is hard to break out into more abstract areas I have no expertise in already.
I can recite and sing from memory and done elaborate comparisons between trans physical and physical senses and played around with time and taking shape of other creatures and genders. I have participated in many healing rituals and energetic exchanges. I have had a few shared lucid dreams with persons I know but that was too weird for me. Having a shared dream environment is probably a great evolutionary leap that some have already made but that I have yet to adjust to. Our minds ( whatever they are) are quite powerful! And such leaps require immense self discipline and high levels of ethical development. Our social media may be preparing us for greater transparency.
As you do have expertise already in science and math I am sure you could incubate a research project. Before bed, jot down some interesting questions, or draw a picture and put it under your pillow and when you wake up in the morning see if you can make sense of your dreams. There may be some clues. I think there are serendipitous events in daylight and nighttime experiences, if we can cultivate the attention. Good luck and may the Force go with you.