“Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.” LyingGroupsTheoryMathematicsComplexesAnalysisEquationsAlgebraComputingDifferential Equations Author:Vladimir Arnold
“The book Dynamic Programming by Richard Bellman is an important, pioneering work in which a group of problems is collected together at the end of some chapters under the heading "Exercises and Research Problems," with extremely trivial questions appearing in the midst of deep, unsolved problems. It is rumored that someone once asked Dr. Bellman how to tell the exercises apart from the research problems, and he replied: "If you can solve it, it is an exercise; otherwise it's a research problem."” IfsImportantBookEndsProblemTogetherGroupsExerciseResearchMathematicsSolveProgrammingMidstChaptersDrsHeadingsAppearingPioneeringUnsolved Problems Author:Donald Knuth
“Images of the world are Renormalization Group fixed points.” WorldScienceGroupsMathematicsFixed Author:David Mumford
“... there are those who believe that mathematics can sustain itself and grow without any further contact with anything outside itself, and those who believe that nature is still and always will be one of the main (if not the main) sources of mathematical inspiration. The first group is identified as "pure mathematicians" (though "purist" would be more adequate) while the second is, with equal inadequacy, referred to as "applied".” IfsFirstsBelieveStillsInspirationWould BeGrowsGroupsSourcePureEqualMathematicsContactMathematicalMathematicianAdequateInadequacy Author:Mark Kac
“There are fields of scientific work...which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology...in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.” MayHas BeensStillsImportantDifferentNextNamesSidesResultsGroupsFieldsPureMathematicsNotionStatisticsEngineeringElectricalDelayedDifferent SidesImportant WorkDifferent NamesElectrical Engineering Author:Norbert Wiener