@article{
 title = {Explosive Proofs of Mathematical Truths},
 type = {article},
 year = {2020},
 identifiers = {[object Object]},
 websites = {http://arxiv.org/abs/2004.00055},
 id = {ea340b57-cd33-3791-86f2-b60fcbdd2be5},
 created = {2020-11-25T00:57:32.270Z},
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 profile_id = {b90fa0f0-b835-3487-8645-24bb43c8aba5},
 group_id = {a91e2012-a2d1-3475-84d1-ff2f8b2ca743},
 last_modified = {2020-11-25T01:02:03.772Z},
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 abstract = {Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because their probability of error grows exponentially as the argument expands. Here we show that under a cognitively-plausible belief formation mechanism that combines deductive and abductive reasoning, mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with four hand-constructed cases from Euclid, Apollonius, Spinoza, and Andrew Wiles. Our results bear both on recent work in the history and philosophy of mathematics, and on a question, basic to cognitive science, of how we form beliefs, and justify them to others.},
 bibtype = {article},
 author = {Viteri, Scott and DeDeo, Simon},
 journal = {arXiv},
 number = {6}
}

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