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This is true. The CS folks are my university tended to be quite strict about writing out quantifiers for everything, while a very accomplished math researcher i

This is true. The CS folks are my university tended to be quite strict about writing out quantifiers for everything, while a very accomplished math researcher in our department told our class to "please write in English" instead of using those symbols, because he wouldn't be able to read them. I asked a friend why he thought this was, and he suspected that the CS department's focus on formal languages and automatic theorem proving is what lead to their use of logical symbols.

lostcolony 9y ago
More computers understand only what they're told. You -have- to be exact. Humans can infer. If it doesn't make sense, they realize something is wrong and attempt to make sense of it. As to why the mathematician preferred 'English', I think it's because quantifiers aren't universal. Mathematical notation itself isn't universal. That is, while the student may be internally consistent and exact in their qualifiers, they are not universally consistent between students, nor with the professor's expectation. The professor wanted to immediately grok what the student was trying to do, not have to approach every single turned in assignment as though it was an unfamiliar mathematical paper, using its own notation, that he had to interpret (where some symbols may share a standard meaning across papers, others won't)
opportune 9y ago
I was this guy to certain professors: at the end of the day it's less about formality and more about someone's ability to understand you at a high level and assess you. To me, I was trying to convey my ideas as precisely as possible. To my professor, I was being so verbose that it would have taken him at least an hour to thoroughly assess the rigor with which I had approach my proof, which simply doesn't scale to all students. Your friend in math is definitions. IME clever definitions minimize the sheer amount of rigor you need to get from point A to point B through their abstractions. The more "natural" or easily understandable a definition is, the easier it is to use that definition as a ground truth in your theorems. For example, I have an unpublished proof of a graph/game-theory conjecture. Proving the theorem's correctness is extremely convoluted if you rely on atomic definitions of graphs, valid actions, etc. However, as you define new relationships precisely, it becomes much easier. The more abstractly you approach the problem, the simpler the problem becomes, given the correct abstractions.
catnaroek 9y ago
I am very much in the math camp, not the computer science camp, but I enjoy annoying mathematicians by explicitly using quantifiers every now and then. Other ways to annoy mathematicians are bringing up pathological examples and remarking that what they have just said doesn't hold in trivial degenerate cases (e.g., the empty set).

lostcolony 9y ago

More computers understand only what they're told. You -have- to be exact. Humans can infer. If it doesn't make sense, they realize something is wrong and attempt to make sense of it. As to why the mathematician preferred 'English', I think it's because quantifiers aren't universal. Mathematical notation itself isn't universal. That is, while the student may be internally consistent and exact in their qualifiers, they are not universally consistent between students, nor with the professor's expectation. The professor wanted to immediately grok what the student was trying to do, not have to approach every single turned in assignment as though it was an unfamiliar mathematical paper, using its own notation, that he had to interpret (where some symbols may share a standard meaning across papers, others won't)

opportune 9y ago

I was this guy to certain professors: at the end of the day it's less about formality and more about someone's ability to understand you at a high level and assess you. To me, I was trying to convey my ideas as precisely as possible. To my professor, I was being so verbose that it would have taken him at least an hour to thoroughly assess the rigor with which I had approach my proof, which simply doesn't scale to all students. Your friend in math is definitions. IME clever definitions minimize the sheer amount of rigor you need to get from point A to point B through their abstractions. The more "natural" or easily understandable a definition is, the easier it is to use that definition as a ground truth in your theorems. For example, I have an unpublished proof of a graph/game-theory conjecture. Proving the theorem's correctness is extremely convoluted if you rely on atomic definitions of graphs, valid actions, etc. However, as you define new relationships precisely, it becomes much easier. The more abstractly you approach the problem, the simpler the problem becomes, given the correct abstractions.

catnaroek 9y ago

I am very much in the math camp, not the computer science camp, but I enjoy annoying mathematicians by explicitly using quantifiers every now and then. Other ways to annoy mathematicians are bringing up pathological examples and remarking that what they have just said doesn't hold in trivial degenerate cases (e.g., the empty set).