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Mathematical notation is not a shorthand for human language. It is a rigorous grammar with properties that make it possible to express very unambiguous qualitie

• rocqua 7y ago
  Mathematical notation can be spoken out loud. Hence, you can include it in a sentence without breaking the flow of that sentence. For the more complicated equations, it becomes harder to unambiguously pronounce them, and the ideas are more separate anyway. Hence we need to break them out. Moreover, I disagree that mathematical notation is a rigorous grammar. Notation is used to be consise, to represent ideas so we can work on them. Precision is only added to resolve ambiguities that are hard to resolve based on the surrounding text. One can make notation fully unambiguous, but that often comes at the cost of consiseness, and thus clarity.
• deleted 7y ago
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• bo1024 7y ago
  I think you're on to an important point, but with some confusion. Mathematical notation is absolutely a shorthand for human language. But the human language it is a shorthand for does have very specific grammar rules governing it for the sentences to be mathematically correct.
• Myrmornis 7y ago
  It actually isn’t a rigorous grammar. Something like Coq or Agda or Mathematica is, but traditional maths notation is full of ambiguities and unclearness that we’re just used to. There’s lots of discussion of this around, including previous HN threads. But if you want a really good example, check out Sussman et al. discussing the Euler Lagrange equations in Structure and Interpretation of Classical Mechanics. Actually here you go, they repeat the same discussion in the preface of this free book: https://www.dropbox.com/s/t3si4b99ijqyhyk/9580.pdf?dl=1 https://www.dropbox.com/s/t3si4b99ijqyhyk/9580.pdf?dl=1