“All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.” FormSimpleResultsMathematicsPropertyMathematicalInvestigationIntegers Author:Leopold Kronecker
“Chaos has come to be associated with the study of anything complex, but, in fact, the mathematical techniques are directly applicable only to simple systems that appear to be complex.” FactsSimpleStudyComplexesChaosTechniqueMathematical Author:Neil Gershenfeld
“The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems -- the determination of the diagonal of a square and that of the circumference of a circle -- revealed the existence of new mathematical beings for which no place could be found within the rational domain.” FirstsTwoProblemFoundSimpleExistenceDeterminationMathematicsCrisisCirclesRationalMathematicalSquaresDomainGeometryArithmeticDiagonal Author:David van Dantzig
“[On Archimedes mathematical results:] It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanation... No investigation of yours would succeed in attaining the proof, and yet, once seen you immediately believe you would have discovered it.” BelieveDifficultSimpleResultsSucceedDiscoveryProofMathematicalExplanationInvestigationGeometryEpiphanyIntricate Author:Proclus
“The Difference Engine can in reality (as has been already partly explained) do nothing but add; and any other processes, not excepting those of simple subtraction, multiplication and division, can be performed by it only just to that extent in which it is possible, by judicious mathematical arrangement and artifices, to reduce them to a series of additions.” Has BeensRealityProcessDifferencesSimpleAddSeriesMathematicalDivisionEnginesArrangementsArtificeMultiplicationSubtraction Author:Ada Lovelace