As AI agents become increasingly capable of generating and optimizing hardware circuits, ensuring the correctness of AI-generated designs becomes more important. Meanwhile, advances in AI lower the barriers to developing and applying formal methods, creating new opportunities to automate and improve hardware verification. This invited paper presents an overview of the methodologies and applications of hardware formal methods in the AI era. First, we examine how agentic AI advances hardware formal methods across three levels: specification, proof construction, and reasoning engines. Second, we discuss how formal methods support reliable AI-driven hardware development through RTL generation, debugging, and correctness-preserving optimization. We review representative research alongside our recent contributions, highlighting key technical advances and insights from experimental results. Finally, we discuss future research opportunities toward proof-native hardware development, where formal reasoning could become an integral part of autonomous hardware design.

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