Computer Proofs Redefine Mathematical Insight

Computer‑assisted proofs (including brute‑force case checks and formal verification) can produce correct answers without the traditional, compact human explanation — and sometimes they generate new concepts only apparent after exhaustive computation. That flips the old hierarchy where conceptual, pen‑and‑paper proofs were the gold standard and forces mathematicians, funders, and the public to decide what counts as understanding and trustworthy evidence. — This reframing affects how science funding, publication standards, and public trust are allocated across disciplines that increasingly rely on automated or AI‑mediated evidence.