alt Hacker NewsI never understood people who preferred traditional math notation (e.g. single letter symbols, weird characters like ∣q⟩ instead of writing down an explicit type, etc.). I guess the main advantage is terseness? To me, the mathematical expressions would be so much easier to understand if they were just written in pseudo code or an actual programming language like Python.
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This 1,000%
Trying to read any math paper is basically like trying to read CodeGolf.
Math notation ultimately is pseudo code just with mostly single letter variables and many operators that are encoded purely by position thus not even requiring a symbol.
Remember that the oft-used e^x is actually an infinite series, even writing it out in summation form would be quite verbose given its frequency in many equations.
You really just get tired of writing/reading "AbstractJavaSerializerBeanFactoryFactoryAbstactMutatorFactoryAccessEnterpriseBeanFactory()" over and over again.
So you and all your peers agree to call that procedure "ẽ"
math notation doesn't bias towards English language understanding like pseudocode
Well, humanity struggled for 2000 years trying to do mathematics without notation, so its benefit is not to be sniffed at. But really it's just an APL-vs-Fortran type debate. They're not fundamentally different. Remember also that Ramanujan had to re-use paper it was so costly/hard to find.
Terseness is a significant advantage in pattern recognition. If you write a long, detailed breakdown of every step, not only are you spending a bunch of time writing, you're also obscuring the natural symmetries of the statement.
It's like saying "I never understood people who prefer to use functions instead of inlining everything". Adding a bunch of visual noise to a statement doesn't improve comprehension.