That sounds good but what I think you're really asking for is an explanation of each of the symbols in their given context and an introduction to the mathematical "jargon" and idioms of the equation's branch of mathematics.
Such things do exist. Unfortunately, they are called "textbooks".
This sounds to me like a pointless exercise. There is a reason for using mathematical notation for non trivial formulas, which is that is more compact and succint, to allow it to convey information efficiently and unambiguously. Think of a formula with a few levels of parentheses; you're not going te be able to express that clearly in a paragraph of text. It's not so much the symbols and notation itself which is hard to grasp, but the mental model of the problem space; once you have that, the formula will usually make sense because you can relate it to this mental model.
I agree to some extent. However, I do think that there is a level of "ramping up" that requires a good bit of teaching and understanding.
It sort of is the members only cigar club of academics. While I can read, understand, and subsequently implement most things in computer science land, when it comes to mathematical notation, there is a lot left to understand.
I think a LOT of people would benefit from a five or six video course simply showing a translation of complex notations to a working algorithm in a popular language, so the commonly used symbols start having meaning.
>There is a reason for using mathematical notation for non trivial formulas, which is that is more compact and succint, to allow it to convey information efficiently and unambiguously.
Maybe, but not always. Remember that Richard Feynman took great issue with how integration was taught in most math classes and devised his own method (inspired from the Calculus for the Practical Man texts).
You can always try to find an even better notation, but the only point I was making is that for certain cases anything is better than a wall of akward text.
No. Feynman never took issue with integration notation or how integration is defined or taught. The story you're referring to is how he learned of a technique for computing integrals that was not covered in schools. The technique is called "differentiation under the integral", and is arguably even more involved.
Not in the context of a length limited conference paper. An implementation adds details for memory allocation and use of data structures &c. This is a distraction in the exposition of an algorithm. It's useful if authors make a well commented implementation available, but the actual paper should contain an abstract definition of the algorithm.
Many mathematical concepts cannot be translated into programming, since computation is by definition discrete. For example, even a simple concept like irrational numbers cannot be completely captured by code.
A better approach might be translating them into more uniform s-expressions. Mathematica does this. You can also check out a similar approach in Structure and Interpretation of Classical Mechanics where tensor expressions are reduced to scheme expressions.
Mathematical symbols are overloaded by context, this could be done but you'd still need to tell it whether it was a formula from "machine learning" or "topology".
Then you'd still fail to account for symbols invented/repurposed in a single paper or by a single author.
Basically, the tool itself is a machine learning problem.
Even the simple case of taking a PDF, finding the first use of any given symbol in that paper, and turning the PDF into an interactive document where hovering on any use of the symbol shows a tooltip showing the first use - now that would be both useful and feasible.
But... the Venn diagram of people able to do such a thing, people motivated to do such a thing (i.e. people reading academic papers who aren't math whizzes), and people with the time to do such a task... seems not to have a sufficient intersection. Most of us in this thread fulfill categories 1 and 2, but not 3... come to think of it, I have work to do... ducks.
Mathematical equations don't have any meaning taken by themselves; they just express a certain relationship between quantities without stating anything specific about what those quantities are.
Any translation of an equation to English would be a certain (usually lossy) interpretation of the equation for some particular quantities. But the same equation can have multiple interpretations in wildly different contexts.
Striking example is quantum mechanics. Physicists in the first half of the 20th century figured out a mathematical model (e.g. the Shroedinger equation) that worked perfectly well for predicting the behaviour of fundamental particles. Interpreting what the equation actually means (let's say in English) proved to be hard though and spawned multiple, sometimes conflicting or paradoxical interpretations. In fact, to this very day physicists are split on their favorite interpretation of QM. On the positive side, the mathematics of QM just works no matter how the result or the calculation are being interpreted.
Yes. If the symbols are in MathML there are accessibility tools which will read them out to you - effectively translating them into plain spoken english.
What you're suggesting is converting a universal, concise, formal language into the potentially ambiguous and/or redundant "plain English". What's the point of that? One has to learn some math before being able to read math.
Such things do exist. Unfortunately, they are called "textbooks".