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Once I spoked to a mathematician about mathematics and he asked me what was my favourite area in Maths. My answer was "Chaos Theory" and he said this is not a discipline in Mathematics.

What is a correct answer to such a question?

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    this is correct there is no such thing as chaos theory.2011-11-16
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    "This question is not a good fit to our Q&A format. We expect answers to generally involve facts, references, or specific expertise; this question will likely solicit opinion, debate, arguments, polling, or extended discussion."2011-11-16
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    I don’t object to *chaos theory* as an informal term for the study of chaotic dynamical systems and related topics.2011-11-16

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For some listing of areas of mathematics: