Does listening to music while studying help or hurt?

It depends on the music and the task, and the popular claim that a particular kind of music makes you smarter is not supported.

The clearest finding concerns lyrics. Language-based tasks, meaning reading, writing and anything involving verbal reasoning, are measurably impaired by music with words, because the lyrics compete for the same processing resources the task requires. This effect is consistent and applies even when you do not feel distracted.

Instrumental music is far less disruptive to verbal work, and for repetitive or procedural tasks, such as practice problems or organising notes, music can help by sustaining arousal and making tedious work more tolerable.

The more important variable is usually what the music is replacing. In a noisy or unpredictable environment, music that masks intermittent noise is an improvement, because unpredictable sound is more disruptive than steady sound. In silence, adding music is more likely to cost than gain for demanding work.

Familiarity matters too. Music you know well demands less attention than something new, which is why a familiar album often works where a discovery playlist does not.

The idea that a particular composer improves cognition originated in a small study about a brief spatial task and was widely misreported. Any effect was short-lived and attributable to mood and arousal rather than anything specific to the music.

The honest practical advice is to test it rather than assume. Do the same kind of task with and without, and compare output rather than how it felt, since the feeling of productivity and actual productivity diverge reliably.