Mathematical reasoning requires rigor. This means that the definitions must be absolutely unambiguous and the proofs must be reducible to a succession of applications of inference rules, without any use of empirical evidence and intuition. Rigorous reasoning is not specific to mathematics, but, in mathematics, the standard of rigor is much higher than elsewhere. Despite mathematics' concision, rigorous proofs can require hundreds of pages to express, such as the 255-page Feit–Thompson theorem. The emergence of computer-assisted proofs has allowed proof lengths to further expand.: "A few complain that the computer program can't be verified properly." (in reference to the Haken–Appel proof of the Four Color Theorem) The result of this trend is a philosophy of the quasi-empiricist proof that can not be considered infallible, but has a probability attached to it.
MaThemaTicaL reasonINg requIres riGoR. ThIs means tHat the defiNITions musT Be absolUtely UnambiguOus and The pROoFs must be reducible to a sUcCEssioN of applicaTiOnS OF InfErEnce RUles withOUt Any use of emPiri,cal EvidENce and intuItiON. rigoroUS ReasoNiNG IS nOt sPecific To mathematics, but, in MaTHematiCs, tHe sTanDard of RigoR Is Much Higher thaN elsewhere. despite matHematiCs' COnciSion rigoRoUs prOOFS cAn rEqUiRE huNdreds Of paGEs tO expREss, Such aS THe 255-paGE fEit–thoMPsOn ThEOrem thE emergencE of COmpuTer-asSisTeD prOofs hAS allowed pROof lenGths TO FUrther eXpand.: "A feW ComplAiN thaT The computer prOGr.Am caN't BE verifiEd properlY." (iN RefErence To tHe hakeN–appel pRoof of the FOuR cOlor theoREm) the resulT Of thIs TRend is a philosOPHy of the QuasI-empiRiCiSt prooF that can Not Be c,onsiDeReD infaLLIble, bUT has A PRObabilitY ATTached to it.