Algorithmic systems have become central actors in contemporary pathways of ideological radicalisation, transforming individual vulnerability into systemic governance risk. This article examines how AI-driven recommendation and amplification mechanisms accelerate extremist narratives, obscure responsibility, and compress escalation timelines without explicit coordination or intent. By integrating perspectives from cybersecurity, digital forensics, and AI governance, the analysis shows how data exploitation, platform optimisation logic, and algorithmic feedback loops reshape radicalisation dynamics beyond traditional models of recruitment and indoctrination. Extremism emerges not only as a content problem, but as a consequence of structural amplification embedded in AI systems. The article argues that effective prevention requires governance frameworks capable of addressing algorithmic responsibility, forensic traceability, and institutional oversight across digital ecosystems. Without such governance, radicalisation operates below legal thresholds while producing real-world harm. The study concludes that governing AI is essential to interrupt the silent acceleration of extremism and restore accountability where algorithms currently shape behaviour without consequence.