The claim
"Islam discourages scientific inquiry and is incompatible with modern science."
The short answer
The Islamic Golden Age (8th–14th century) produced foundational advances in algebra, optics, medicine, astronomy, and chemistry. The Quran repeatedly encourages observation of the natural world, and the Prophet ﷺ emphasized the obligation of seeking knowledge.
Evidence-Based Clarification
The Quran Commands Reflection on the Natural World
The Quran repeatedly points to natural phenomena as signs, urging believers to observe, reflect, and reason. The first word revealed was 'Iqra' (Read/Recite). Muslim scholars invented algebra (Al-Khwarizmi), advanced optics (Ibn al-Haytham), pioneered surgical techniques (Al-Zahrawi), and preserved and transmitted Greek philosophical and scientific works to Europe during a period when they were otherwise lost.
PRIMARY SOURCES (2)
"Read in the name of your Lord who created. Created man from a clinging substance. Read, and your Lord is the most Generous. Who taught by the pen. Taught man that which he knew not."
اقْرَأْ بِاسْمِ رَبِّكَ الَّذِي خَلَقَ
— Surah Al-Alaq 96:1-5check the original
"Indeed, in the creation of the heavens and the earth and the alternation of the night and the day are signs for those of understanding — who remember Allah while standing or sitting or [lying] on their sides and give thought to the creation of the heavens and the earth."
إِنَّ فِي خَلْقِ السَّمَاوَاتِ وَالْأَرْضِ وَاخْتِلَافِ اللَّيْلِ وَالنَّهَارِ لَآيَاتٍ لِّأُولِي الْأَلْبَابِ
— Surah Aal-Imran 3:190-191check the original