“I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.” CertainRealizingViewsNumbersOpinionInfiniteMathematicalOppositionUndertakings Author:Georg Cantor
“The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.” MindFormSeeingPossibilityHighestLogicInfiniteCertaintyUncertaintyReasoningInfinityOntologyMyopia Author:Georg Cantor
“Mathematics, in the development of its ideas, has only to take account of the immanent reality of its concepts and has absolutely no obligation to examine their transient reality.” IdeasRealityDevelopmentConceptsAccountsMathematicsObligationTransient Author:Georg Cantor
“There is no doubt that we cannot do without variable quantities in the sense of the potential infinite. But from this very fact the necessity of the actual infinite can be demonstrated.” FactsDoubtInfiniteNo DoubtQuantityVariables Author:Georg Cantor
“The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.” YearsStepsGroupsConceptsMathematicsMathNonsenseIntroductionCiphers Author:Alexander Grothendieck
“A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it... yet finally it surrounds the resistant substance.” DifferentSeemsHappensEarthMovingWaterKnownWeekSeaSurroundResistingPenetrationUnknown Things Author:Alexander Grothendieck
“Discovery is the privilege of the child: the child who has no fear of being once again wrong, of looking like an idiot, of not being serious, of not doing things like everyone else.” ChildrenSeriousDiscoveryPrivilegeIdiotNo FearHave No Fear Author:Alexander Grothendieck
“I am a Christian which means that I believe in the deity of Christ, like Tycho de Brahe, Copernicus, Descartes, Newton, Leibnitz, Pascal… like all great astronomers mathematicians of the past.” BelieveMeanChristianPastI BelieveChristI Believe InMathematicianDeitiesNewtonAstronomersPascalCopernicusChrist Like Author:Augustin-Louis Cauchy
“I know many people who believe in a god, and I expected to find him on my way to the South Pole if he exists. My religious experiences were very different however, [only] involving myself, nature and the universe.” PeopleIfsKnowsWayBelieveDifferentUniverseReligiousSouthExpectedMy WayInvolvingReligious Experience Author:Liv Arnesen
“Is it not true, then, that my life with all its limitation touches at many points the life of the World Beautiful? Everything has its wonders, even darkness and silence, and I learn, whatever state I may be, therein to be content.” WorldMayStatesBeautifulSilenceWonderDarknessLimitation Author:Anne Sullivan Macy