Is it permissible to study and teach theoretical mathematics that has no real-world applications and is of no benefit to a person in their daily life, knowing that the Prophet, peace and blessings be upon him, used to seek refuge in Allah from knowledge that does not benefit?

There is no harm in studying beneficial worldly sciences, and a believer is rewarded for it if he intends to benefit Muslims through it. This knowledge may even be obligatory. Al-Ghazali explained that sciences are divided into religious (Shar'i) and non-religious, and that praiseworthy non-religious sciences related to worldly interests, such as medicine and accounting, may be a collective obligation (fard kifaya) that is indispensable for the sustenance of worldly affairs. Similarly, the fundamentals of crafts like agriculture and weaving, among others, are also collective obligations. Therefore, there is no harm in studying theoretical mathematics; rather, it has benefits and advantages.