That's precisely how I learned that formula. In fact that's basically the pedagogy that's been presented to me for almost all the mathematics I've learned.
Sets? Define a set semantically, then replace "set" with S. Vector spaces? Define a vector space semantically, then replace "vector space" with V. Limits? Define a limit semantically, then replace the word with "lim".
Moreover mathematicians typically use jargon in a more reader-friendly way than simply throwing obtuse equations at them. Expressions, equations, inequalities and identities are complements to the proof, not the proofs themselves. Best practice holds that you present a theorem in plain language alongside the necessary notation, then break its proof down into as many atomic units (lemmas, propositions, corollaries, etc) as possible. Here is a blog post[1] from Terence Tao giving general advice for why that's useful. Tao has written a bunch[2] of these on the theme of emphasizing exposition and clarity.
Also contrary to popular belief, well-written mathematics papers actually have quite a lot of exposition in them. For a famous example, look at Yitang Zhang's proof[3] that there are infinitely many primes with 70 million numbers (or fewer) in between them. He spends a full five pages on introduction, background results used to develop the proof, and (most importantly) notation. He also includes a "sketch" of the proof in broad strokes so that a reader can follow his arguments at both a high level and in gritty detail.
That doesn't mean papers like Zhang's are accessible to most people. The jargon is still there and you can't really change that unless you want papers to become self-contained monographs. But the point is that what you're proposing - concepts defined in a straightforward way before moving on to dense notation - is already the general practice.
Sets? Define a set semantically, then replace "set" with S. Vector spaces? Define a vector space semantically, then replace "vector space" with V. Limits? Define a limit semantically, then replace the word with "lim".
Moreover mathematicians typically use jargon in a more reader-friendly way than simply throwing obtuse equations at them. Expressions, equations, inequalities and identities are complements to the proof, not the proofs themselves. Best practice holds that you present a theorem in plain language alongside the necessary notation, then break its proof down into as many atomic units (lemmas, propositions, corollaries, etc) as possible. Here is a blog post[1] from Terence Tao giving general advice for why that's useful. Tao has written a bunch[2] of these on the theme of emphasizing exposition and clarity.
Also contrary to popular belief, well-written mathematics papers actually have quite a lot of exposition in them. For a famous example, look at Yitang Zhang's proof[3] that there are infinitely many primes with 70 million numbers (or fewer) in between them. He spends a full five pages on introduction, background results used to develop the proof, and (most importantly) notation. He also includes a "sketch" of the proof in broad strokes so that a reader can follow his arguments at both a high level and in gritty detail.
That doesn't mean papers like Zhang's are accessible to most people. The jargon is still there and you can't really change that unless you want papers to become self-contained monographs. But the point is that what you're proposing - concepts defined in a straightforward way before moving on to dense notation - is already the general practice.
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1. https://terrytao.wordpress.com/advice-on-writing-papers/crea...
2. https://terrytao.wordpress.com/advice-on-writing-papers/
3. http://annals.math.princeton.edu/2014/179-3/p07