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" "It is almost impossible for me to read contemporary mathematicians who, instead of saying “Petya washed his hands,” write simply: “There is a <math>t_1<0</math> such that the image of <math>t_1</math> under the natural mapping <math>t_1 \mapsto {\rm Petya}(t_1)</math> belongs to the set of dirty hands, and a <math>t_2</math>, <math>t_1<t_2 \leq 0</math>, such that the image of <math>t_2</math> under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.”
Vladimir Igorevich Arnold (alternative spelling Arnol'd, Russian: Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Russian mathematician famous for his work on the KAM theorem regarding the stability of integrable systems, who made important contributions in dynamical systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics and singularity theory.
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When you are collecting mushrooms, you only see the mushroom itself. But if you are a mycologist, you know that the real mushroom is in the earth. There's an enormous thing down there, and you just see the fruit, the body that you eat. In mathematics, the upper part of the mushroom corresponds to theorems that you see. But you don't see the things which are below, namely problems, conjectures, mistakes, ideas, and so on. You might have several apparently unrelated mushrooms and are unable to see what their connection is unless you know what is behind.