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PAUL HALMOS Celebrating 50 Years of Mathematics: Celebrating 50 Years of Mathematics

This book is a compilation of essays and reflections on the mathematical work of Paul Halmos, a renowned mathematician, focusing on his contributions over five decades. more

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Paul Halmos
Paul Halmos

Paul Halmos was a renowned mathematician known for his contributions to functional analysis and probability theory. His research had a profound impact on the development of modern mathematics. more

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“The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.”

SelfReasonUseLanguagePrinciplesLogicMathematicsAbandonPropositionsUtteranceAnalyticsSinningContradictingUse Of LanguageTautology
Author:A.J. Ayer
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“The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end.”

HumansLittlesEndsSciencePurposeStudyActivityMathematicsDuesMathematicalInevitableExpertsInquiryDeliberateUsefulnessHuman ActivitySaturatedDrawbacksTechnicalities
Author:Herbert Turnbull
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“The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.”

IfsWorldMatterSubjectsEternalLogicMathematicsIndependentMathematicalPropositionsSubject MatterValidity
Book:The pastures of wonder: the realm of mathematics and the realm of science
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“There have been many authorities who have asserted that the basis of science lies in counting or measuring, i.e. in the use of mathematics. Neither counting nor measuring can however be the most fundamental processes in our study of the material universe-before you can do either to any purpose you must first select what you propose to count or measure, which presupposes a classification.”

FirstsHas BeensUseLyingPurposeUniverseProcessCan DoStudyMaterialsAuthorityBasesMathematicsFundamentalsCountingProposeSelectMeasurementMeasuringClassification
Book:Classification and Biology
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