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proof abundance
also era of proof abundance
Definition of proof abundance
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: a condition in which AI systems can produce mathematical proofs or credible proof attempts faster than people and institutions can verify, understand, explain, review, and incorporate them into mathematics
- Proof abundance shifted the department's bottleneck from finding candidate solutions to deciding which machine-generated arguments deserved human attention.
- The journal introduced new disclosure and verification rules for an era of proof abundance.
Two meanings, one word
In everyday English
Abundance is a very large or more-than-sufficient supply of something.
In AI
A condition in which AI systems can produce mathematical proofs or credible proof attempts faster than people and institutions can verify, understand, explain, review…
Origin & history
Mathematician Terence Tao popularized the expression in 2026 when discussing how increasingly capable AI systems could move mathematics from proof scarcity to proof abundance. He developed the idea in his July International Congress of Mathematicians lecture and returned to it in an October talk titled Math 2.0, after a surge of AI-generated mathematical results intensified debate over verification, exposition, and research incentives.
Test yourself
Which of these is the meaning of proof abundance?
Cite this entry
"Proof abundance." AI Dictionary, Dadgogo, https://dadgogo.com/dictionary/proof-abundance/. Accessed 13 Oct. 2026.