We Live in the Dependently Typed Future Now (www.stephendiehl.com)

Recent advancements in AI and mathematics have ushered in what many are calling a "dependently typed future." Over a month, OpenAI and other researchers achieved significant milestones, including formalizing Fermat's Last Theorem in Lean, proving Khot's Unique Games Conjecture, and releasing 372 new mathematical results on GitHub. The implications are profound: AI-driven type checkers can now quickly verify complex mathematical proofs, with Lean being central to this shift. These advancements not only showcase the potential for AI to tackle historically challenging problems but also suggest an upcoming transformation in how mathematical work is conducted, making human understanding a luxury as machine-verified results flood in at unprecedented rates. At the forefront of this change is the new tool nano-lean, a fast type checker capable of verifying the entire Mathlib library in just under twelve seconds. The tool's efficiency stems from bypassing time-consuming parsing steps typically involved in code verification, achieving a remarkable speed that aligns well with AI's capability to generate proofs swiftly. As AI systems increasingly blend mathematical inference with dependent types, concerns arise regarding the reliability and interpretability of this output. The advent of nano-lean emphasizes the urgent need for effective verification tools to ensure that precision and trust are maintained in a rapidly evolving landscape where AI could redefine the role of mathematicians.