✅ Answer: Please pay attention to the following narrations:

1 عن إبراهیم بن عبدالحمید عن أبی الحسن موسی (علیه السلام) قال: دخل رسول الله صلی الله علیه و آله المسجد فإذا جماعة قد أطافوا برجل فقال ما هذا فقیل علامة فقال و ما العلامة فقالوا له أعلم الناس بأنساب العرب و وقائعها و أیام الجاهلیة و الأشعار العربیة قال فقال النبی صلی الله علیه و آله ذاک علم لا یضر من جهله و لا ینفع من علمه ثم قال النبی صلی الله علیه و آله إنما العلم ثلاثة آیة محکمة أو فریضة عادلة أو سنة قائمة و ما خلاهن فهو فضل.

📚 Al-Kafi vol.1 p.32

Imam Kazim (peace be upon him) said: The Messenger of Allah (peace be upon him and his family) entered the mosque and saw people gathered around a man. The حضرت (prophet) said: 'What is this?!' It was said: 'He is an 'allama'!' He said: 'What is an 'allama'?!' They said: 'He is the most knowledgeable of people about the lineages of the Arabs and their events, the days of ignorance, and Arabic poetry!' The حضرت (prophet) said: 'This is a knowledge that whoever does not know it, it does not harm him, and whoever knows it, it does not benefit him!'

2 عَنْ جَمِیلٍ عَنْ أَبِی عَبْداللَّهِ قَالَ سَمِعْتُهُ یَقُولُ مَنَّ اللَّهُ عَلَی النَّاسِ بَرِّهِمْ وَ فَاجِرِهِمْ بِالْکِتَابِ وَ الْحِسَابِ وَ لَوْ لَا ذَلِکَ لَتَغَالَطُوا.

Then the Prophet (peace be upon him and his family) said: 'Indeed, knowledge is three things: a firm verse, a just duty, and an established tradition, and what is other than these is an excess (not knowledge)!'

📚 Al-Kafi vol.5 p.155

3 قَالَ أَمِيرُالْمُؤْمِنِينَ : الْعُلُومُ أَرْبَعَةٌ الْفِقْهُ لِلْأَدْيَانِ وَ الطِّبُّ لِلْأَبْدَانِ وَ النَّحْوُ لِلِّسَانِ وَ النُّجُومُ لِمَعْرِفَةِ الْأَزْمَانِ

Jamil said: I heard Imam Sadiq (peace be upon him) say: Allah bestowed a favor upon the righteous and the wicked of people by writing and calculation, and if it were not for that, they would lead each other to wrong and error!

📚 Ma'dan al-Jawahir p.40

4 عَنْ سَعِیدِ بْنِ مُحَمَّدٍ الطَّاهری عَنْ أَبِیهِ عَنْ أَبِی عَبْداللَّهِ قَالَ: سَأَلَهُ رَجُلٌ عَنْ بَیْعِ الْجَوَارِی الْمُغَنِّیَاتِ فَقَالَ شِرَاؤُهُنَّ وَ بَیْعُهُنَّ حَرَامٌ وَ تَعْلِیمُهُنَّ کُفْرٌ وَ اسْتِمَاعُهُنَّ نِفَاقٌ.

Amir al-Mu'minin (peace be upon him) said: Knowledge is four things: the science of jurisprudence for religions, the science of medicine for bodies, the science of grammar for languages, and the science of astronomy for knowing the times!

📚 Al-Kafi vol.5 p.120

5 عَنْ أَبِی الْبَخْتَرِیِّ عَنْ جَعْفَرِ بْنِ مُحَمَّدٍ عَنْ أَبِیهِ أَنَّ عَلِیّاً قَالَ: مَنْ تَعَلَّمَ شَیْئاً مِنَ السِّحْرِ قَلِیلًا أَوْ کَثِیراً فَقَدْ کَفَرَ وَ کَانَ آخِرَ عَهْدِهِ بِرَبِّهِ وَ حَدُّهُ أَنْ یُقْتَلَ إِلَّا أَنْ یَتُوبَ.

A man asked Imam Sadiq (peace be upon him) about the buying and selling of singing slave girls; the Imam said: Buying and selling them is forbidden, teaching them (ghina - singing) is disbelief, and listening to them is hypocrisy!

📚 Qurb al-Isnad p.71

6 قال امیرالمؤمنین في حديث... أَیُّهَا النَّاسُ إِیَّاکُمْ وَ تَعَلُّمَ النُّجُومِ إِلَّا مَا یُهْتَدَی بِهِ فِی بَرٍّ أَوْ بَحْرٍ...

Amir al-Mu'minin (peace be upon him) said: Whoever learns something of magic, whether little or much, has certainly disbelieved, and his last covenant is with his Lord, and his punishment is to be killed, unless he repents!

📚 Nahj al-Balagha

7 قال امیرالمؤمنین : رُبَّ عِلْمٍ أدَي إلَي مَضَلَتِكَ

Amir al-Mu'minin (peace be upon him) said in a hadith: O people! Avoid learning the science of astronomy, except for the amount with which you can find your way on the sea and land!

📚 Ghurar al-Hikam no. 1679

Amir al-Mu'minin (peace be upon him) said: How much knowledge there is that leads to your misguidance!

8 Amir al-Mu'minin (peace be upon him) said: Teach your sons swimming and archery!

📚 Al-Kafi vol.6 p.47

✅ According to the above narrations and others, the things worthy of the name of 'knowledge' are limited to things such as the Quran, the science of religious duties and traditions, the science of jurisprudence, the science of medicine, the science of grammar (to the extent of need), and the science of astronomy to the extent of knowing times and prayer times and finding one's way on sea and land.

The teaching of some sciences, such as magic and singing and the like, is explicitly forbidden.

Other areas of knowledge such as mathematics and writing and swimming and archery have been encouraged, although they are not worthy of the name of 'science'.

اللَّهُمَّ صَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْر

✅ But in general, any useful knowledge, such as history, physics, and chemistry, etc., which does not have a specific or general prohibition and does not lead to misguidance, although it is not worthy of the name of 'science', is considered a virtue (or an excess).