Quotable Math @QuotableMath
Quotable Mathematics - Quotes and Resources related to Mathematics, (Mathematical) Sciences and Mathematicians quotablemath.blogspot.com Cologne Joined November 2014-
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"[In modern #math] there is a strong tendency towards formulations of concepts that minimise the number and significance of arbitrary choices. This crispness tends to emphasise the naturality of the construction or definition, at the expense sometimes of accessibility." T Gannon
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"Men of #science have made abundant #mistakes of every kind; their #knowledge has improved only because of their gradual abandonment of ancient #errors, poor #approximations, and premature #conclusions." George Sarton, 1959 #quotes
"#Measurement [.] always has an element of #error in it. The most exact description or #prediction that a scientist can make is still only approximate." Abraham Kaplan, 1964 #math #quotes #approximation
"Mathematical #programming (or #optimization" #theory) is that branch of #mathematics dealing with techniques for maximizing or minimizing an #objective #function subject to linear, nonlinear, and integer constraints on the variables." George B Dantzig et al, 1997 #math #quotes
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Understanding probability is essential in data science. In 4 minutes, I'll demolish your confusion. Let's go!
"In most #engineering #problems, particularly when solving #optimization problems, one must have the opportunity of comparing different variants quantitatively. It is therefore important to be able to state a clear-cut quantitative #criterion." Yakov Khurgin, 1974 #math #quotes
"A #pattern is a #design or #model that helps grasp something. Patterns help connect things that may not appear to be connected. Patterns help cut through #complexity and reveal simpler understandable #trends." Anil K Maheshwari, 2015 #science #quotes #understanding #simplicity
"Statistical #models for #data are never true. The question whether a model is true is irrelevant. A more appropriate question is whether we obtain the correct scientific conclusion [.]" Scott Zeger, 1991 #science #statistics #quotes
"[.] it is not enough to say: 'There's #error in the #data and therefore the study must be terribly dubious'. A good critic and data analyst must do more: he or she must also show how the error in the #measurement or the #analysis affects the #inferences made [.]" E R Tufte, 1974
"You can very generally think of a #manifold as a #space which is locally #Euclidian - that means that if you look closely enough at one small part of a manifold then it basically looks like Rn for some n." Jon P Fortney, 2018 #math #quotes #geometry quotablemath.blogspot.com/2024/12/on-man…
"The self-similarity on different #scales arises because growth often involves #iteration of simple, discrete #processes (e.g. branching). These repetitive processes can often be summarized as sets of simple #rules." David G Green, 2000 #math #quotes #similarity
"The peculiarity of [...] statistical #hypotheses is that they are not conclusively refutable by any #experience." Richard B Braithwaite, 1953 #statistics #quotes quotablemath.blogspot.com/2024/11/on-hyp…
"#Science consists simply of the formulation and testing of #hypotheses based on observational #evidence; #experiments are important where applicable, but their function is merely to simplify #observation by imposing controlled #conditions." Henry L Batten, 1971 #quotes
"#Mathematics is not about abstract entities alone but is about relation of abstract entities with real entities. […] Adequacy relations between abstract and real entities provide space or opportunity where mathematical and logical #thought operates parsimoniously." N Singh 2005
"[.] the argument from #parsimony is really no argument at all - it typically functions only to shut down more interesting discussion. If history is any guide, it's never a good idea to assume that a scientific #problem is cornered." D Eagleman 2011 #math quotablemath.blogspot.com/2024/12/occams…
"In many instances, a picture is indeed worth a thousand words. [.] Naive #pictures are often extremely helpful, but more sophisticated pictures can be both simple and even more informative." John W Tukey et al, 1966 #dataviz #statistics #simplicity quotablemath.blogspot.com/2024/11/the-dr…
"[.] we must not measure the #simplicity of the #laws of #nature by our facility of conception; but when those which appear to us the most simple, accord perfectly with #observations of the #phenomena, we are justified in supposing them rigorously exact." P-S Laplace,1809 #quotes
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