“The new painters do not propose, any more than did their predecessors, to be geometers. But it may be said that geometry is to the plastic arts what grammar is to the art of the writer. Today, scholars no longer limit themselves to the three dimensions of Euclid. The painters have been lead quite naturally, one might say by intuition, to preoccupy themselves with the new possibilities of spatial measurement which, in the language of the modern studios, are designated by the term fourth dimension.” MayHas BeensArtSaidMightTodayThreeLanguageTermModernPossibilityLimitsLogicStudiosIntuitionPainterCertaintyUncertaintyReasoningDimensionsScholarFourthPlasticGrammarProposeMeasurementGeometryPredecessorsOntologyNew PossibilitiesSpatialEuclidThree Dimensions Author:Guillaume Apollinaire
“Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.” MayProblemResultsKnownPiecesMysteryBuiltLogicMathematicsSolveProofCertaintyUncertaintyIslandsReasoningIngredientsSpeculationOntologyTheoremsUnanswered QuestionsUnanswered Author:Ivars Peterson
“It is true that of far the greater part of things, we must content ourselves with such knowledge as description may exhibit, or analogy supply; but it is true likewise, that these ideas are always incomplete, and that at least, till we have compared them with realities, we do not know them to be just. As we see more, we become possessed of more certainties, and consequently gain more principles of reasoning, and found a wider base of analogy.” KnowsMayIdeasRealityFoundPrinciplesKnowledgeGreaterGainsCertaintyReasoningDescriptionPossessedIncompleteExhibitsAnalogies Book:The Works of Samuel Johnson, LL. D.: Lives of the poets Source: The Works of Samuel Johnson, LL. D.: Lives of the poets
“Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems-general and specific statements-can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.” MayScienceDealsPracticeActivityIntellectualAccountsMathematicsStartingStatementsQueensAssumptionReasoningLogicalCountingMeasuringArithmeticTheoremsLogical Reasoning Author:Christopher Zeeman