I am at the beginning of studying Bach and starting with 18 little preludes, specifically BWV 924. The reason I am starting with Bach is that after much research, I find he really is the daddy of it all by having a mathematical approach to music. However, I am struggling to choose how to use the sustain pedal. Tried several combinations but somehow, I am not entirely satisfied with my choices. Does Bach mathematical approach mean it has to be used at a specific moment or should I choose when to use it? Is this the only bit I can choose to express how I feel the music or not? Since he is mathematically inclined, I want to check to do it right! See my confusion?
Bach did not have a sustain pedal. When playing fugues, it tends to be quite useless since it will affect themes in different state of progress. For some preludes of very simple structure, it may work out.
Basically if you cannot figure out a consistent use of the sustain pedal, not using it may be the best option.
Although user35465 is technically correct, it is very difficult to find a Bach recording (by a pianist) in which no sustain pedal is used.
When playing fugues, it tends to be incredibly useful because the sustain pedal enables you to play legato in places where the fingering doesn't allow you to do so.
Of course, Bach didn't have a sustain pedal and because of this, wouldn't have used it. On the other hand, modern pianists (including those with a more historical approach to Bach's music) tend to use the sustain pedal. Not to sustain harmonies (as is common in romantic works), but to help connect the voice leading. These two are very different (and I imagine it's not easy to hear the second type of pedalling).
Basically, you're playing Bach on the wrong instrument (a piano, rather than a harpsichord1). Because of this, you'll have to compromise - it's impossible to play Bach's harpsichord works like Bach intended on anything but a harpsichord, so use the instrument you chose instead. Although Bach had access to the early fortepianos at the end of his life, he didn't like them and kept to the harpsichord.
1: Bach also very much liked to play the clavichord. For the purposes of this answer, this doesn't really change anything, so I'll leave it be. Thanks to reinierpost for pointing out the omission.
After all these comments, here are my thoughts: I will not use the sustain pedal when studying Bach because: 1- he didn't have one therefore I am not getting one. 2- I will not compromise my technical challenges by using the pedal 3- I will only use the pedal at my discretion when I feel it's needed playing artist who had one. 4- I don't have a harpsichord and I am unlikely to use one therefore I will explore the sounds I can produce to get as close as possible to the original sounds. 5- I will however continue to practise and explore the use of the sustain pedal with different level fingering to produce different sounds. That's the beauty of the piano, it can mimic all instruments if used properly. A friend of mine loves Debussy and he loves it so much that when he plays some of his pieces, it sounds like bell ringing, like a gamalong.