When formalising a proof costs no more than writing it, mathematics will flip: papers written in Lean first, and journals refereeing only for significance because correctness is certified.

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  Formalising a proof in Lean currently takes about ten times the effort of writing it out: doable, but annoying.

  The prediction that mathematics flips to Lean-first papers is a claim about a cost falling, and the cost it names is the one Tao measures today: roughly ten times the effort of writing the proof out. The flip is the same sentence with that number set to one.

Shared subject first, then similar wording. They may agree or disagree.

• AI-written code makes formal proof necessary, because human review of all that generated code becomes the bottleneck. MKMartin Kleppmann22 Apr 2026formal proof
• Formal verification is about to become economical, because models are getting good enough at writing the proofs that humans no longer have to. MKMartin Kleppmann22 Apr 2026formal proof
• Full formal verification is a waste of money for most software: near-perfect is reachable with ordinary techniques at a fraction of the cost. HWHillel Wayne21 Jan 2019formal proof
• Nuclear power plants, the standard example of software that must be proved correct, do not care about formal verification: thorough testing is enough for them. HWHillel Wayne29 Jul 2026formal proof
• A persistently rising dividend yield eventually forces capital appreciation as the market rerates the stock. SBSanjay Bakshi3 Mar 2026mathematics

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