“The practice of first developing a clear and precise definition of a process without regard for efficiency, and then using it as a guide and a test in exploring equivalent processes possessing other characteristics, such as greater efficiency, is very common in mathematics. It is a very fruitful practice which should not be blighted by premature emphasis on efficiency in computer execution.” ShouldFirstsProcessCommonPracticeClearGreaterComputerTestsRegardMathematicsDefinitionsGuidesDevelopingCharacteristicsExecutionEfficiencyExploringPreciseEmphasisPossessingPremature Author:Kenneth E. Iverson
“If there be some who, though ignorant of all mathematics . . . dare to reprove this work, because of some passage of Scripture, which they have miserably warped to their purpose, I regard them not, and even despise their rash judgement.” IfsPurposeRegardMathematicsDareScriptureIgnorantJudgementPassagesDespise Author:Nicolaus Copernicus
“When, therefore, I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world-machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere.” WorldLongMovementMachinesRegardMathematicsPhilosopherDetailsTraditionalUncertaintyExplanationSpheresWearyDefiniteBehalfSystematicBuilder Author:Nicolaus Copernicus
“Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.” ImportantMatterPlayFactsScienceNatureKnownKnowledgeDevelopmentConnectionsRegardMathematicsComplexesConnectedMathematicalLimitationAnalysisComplexityAssemblageInquirersMathematical Analysis Author:Oliver Heaviside
“As regards authority I so proceed. Boetius says in the second prologue to his Arithmetic, 'If an inquirer lacks the four parts of mathematics, he has very little ability to discover truth.' And again, 'Without this theory no one can have a correct insight into truth.' And he says also, 'I warn the man who spurns these paths of knowledge that he cannot philosophize correctly.' And Again, 'It is clear that whosoever passes these by, has lost the knowledge of all learning.'” IfsMenLittlesTruthLostAbilityPathClearFourHe ManTheoryAuthorityRegardMathematicsInsightArithmeticPrologueInquirers Book:Opus Majus, Volumes 1 and 2 Source: Opus Majus, Volumes 1 and 2
“Only in mathematics and physics was I, through self-study, far beyond the school curriculum, and also with regard to philosophy as it was taught in the school curriculum.” SelfPhilosophySchoolStudyTaughtRegardMathematicsPhysicsCurriculumSchool Curriculum Book:The Ultimate Quotable Einstein Source: The Ultimate Quotable Einstein