The rapid expansion of artificial intelligence (AI), datafication, and the emergence of the algorithmic society have posed significant theoretical challenges to the conventional understanding of progress. The central question of this study is how the concept of progress in Islamic thought can be redefined in the age of the algorithmic society. The study aims to reinterpret the Islamic concept of progress and to develop a conceptual framework that explains the relationship between Islamic values and intelligent technologies. This is a fundamental qualitative study employing Reflexive Thematic Analysis (Braun & Clarke), supported by documentary and conceptual analysis. The data were collected from the Holy Qur'an, Nahj al-Balagha, selected Hadiths, Sahifeh-ye Imam Khomeini, the speeches and writings of Ayatollah Khamenei, the Islamic-Iranian Model of Progress, and a range of authoritative scholarly sources on Islamic thought, artificial intelligence, and the algorithmic society. The findings reveal that Islamic progress in the algorithmic age is structured around six overarching themes: human-centered progress, justice-oriented progress, ethics-oriented progress, guided technological progress, Islamic intelligent governance, and civilization-building. Within this framework, technology and AI are regarded not as ends in themselves but as instruments for promoting justice, preserving human dignity, and strengthening civilizational independence. The study concludes that achieving Islamic progress in the intelligent age requires value-oriented governance of technology, responsible governance of data and algorithms, and the reinforcement of scientific and technological self-reliance. The principal contribution of this research is the introduction of the conceptual framework of "Guided Technological Progress" as a theoretical foundation for Islamic intelligent governance and the realization of the New Islamic Civilization.