I am actually a newbie and wondering of the level of consciousness during the LD. To make the question simple, can the highest level of LD continue his/her consciousness as in his daily life? For example, before you go to sleep, look at the equation below
1+23+45+67+89+1011+1213+1415+1617+18*19+20=?
IF you can continue you awareness in the LD, you can easily remember the equation to solve. and IF you have the consciousness slightly compatible to day life, you can solve the equation in the LD and remember the answer when wake up…
So can anyone do it here?
Welcome jedynet 
Mathematics is generally believed to be Quite difficult , but MAYBE some can do it … but as i said , its doubtable …
You wouldn’t require a high level lucid, just enough lucidity to take control long enough to work it out. If you are capable of answering it in WL then it shouldn’t be an issue in an LD so long as you can maintain your focus.
But to be honest, I’d have trouble just remembering that equation in five minutes time let alone remembering it in my sleep.
I cant say i have ever done that question before or anything quite like it,…b ut i have done advanced algerba and other math in my dreams. TVM etc etc. I didnt understand the work in clss all that well so i lucid dreamed it, over the space of week i had 5 math dreams and they were all very very complex, i understood them well in my dreams but upon waking up i couldnt remember much, but, next week in math, with no study at all, the work was easy and i got very good mark on my test that semester…mind you i didnt really enjoy the math dreams so i didnt do it again…well not often. Its possible, but remembering the new thigns you learn can be haarder
There is an ancedote about a scientist that dreamt about circling snakes, and when he woke up he understood it was a dream about the shapes of certain molecules.
So yes, theoraticlly (And as TimeLess shown - practicly) You can memorize and have better understandment of things in dreams.