Psychology (aesthetic, creativity and intuition) The validity of a mathematical theorem relies only on the rigor of its proof, which could theoretically be done automatically by a computer program. This does not mean that there is no place for creativity in a mathematical work. On the contrary, many important mathematical results (theorems) are solutions of problems that other mathematicians failed to solve, and the invention of a way for solving them may be a fundamental way of the solving process. An extreme example is Apery's theorem: Roger Apery provided only the ideas for a proof, and the formal proof was given only several months later by three other mathematicians.
pSychologY (AEsThETic, creativitY and IntuItIOn) the vAlidity of A MatHeMatiCaL tHeorEm relIeS ONlY On the rIgOr of its Proof, whiCh couLd tHeoreTiCalLy be donE AuTOmatiCAlly by a cOmpUTEr pRogram. this dOes nOt meaN THat thErE is nO place foR CREAtivItY in A Mathematical woRk. On THE cONtRaRy, mAnY imPorTant maThemaTIcal rEsultS (thEOreMs) Are solutIoNs OF probleMs ThaT oThER mathemAticIanS faiLed To SOlVe, anD THe invenTION Of a Way fOr sOlvIng TheM maY bE a fUndamEntaL way Of The solVing PrOcess. an eXtremE EXample iS aperY's tHeOReM: roGer aPery proviDEd only tHe IdEAs foR a ProoF, And the FORmal pRoof was GIven ONly SeVEral monthS lateR by THrEE oTHer mathEMaTicIANs.