Ask HN: How did you learn math notation?

Use the 3 line version of approximately equal (looks like tilde above an equal sign, ≅).

1. You're reading a journal article. They will assume you know the notation not just of the broader discipline (e.g. physics/electrical engineering), but of the subdiscipline and at times the subsubdiscipline. Journal papers are explicitly written not to be easy to comprehend by beginners.[1] Notation will be only one problem you'll face.

2. As has been pointed out, this is not a mathematics paper. Mathematicians have their own notation, as do physicists and engineers. As I mentioned in the above bullet, they can have their own notation even in subdisciplines (e.g. circuit folks use "j" for the imaginary number, and semiconductor folks use "i"). There is a lot of overlap in notation amongst these parties, but you should never assume because you know one notation that you'll easily understand the math written by other fields.

3. Most introductory textbooks will explain the basic notation. Unfortunately, I often do find gaps where you go to higher level textbooks and they use notation that they don't explain (i.e. they assume you've seen it before), but is not covered in the prior textbooks.

4. Finally, sorry to say this, but "delta" (the triangle) for representing change is used in almost all sciences and engineering. It was heavily used in my high school as well. If you're struggling with this you really need to read some introductory textbooks in, say, physics.

[1] I'm not kidding. I've spent time in academia and I've complained how obtuse some articles are, and almost universally the response is "We write for other experts, not for new graduate students". One professor took pride at the fact that in his field, one can comprehend only about one page of a paper per day - and this coming from someone who is an expert. These people have issues.

2] dive deep into the history of math.

3] youtube… 3 blue 1 brown, stand up maths, numberphile, kahn academy. These channels are your friends.

4] don’t give up and make it fun. Once you’re bit by the bug of curiosity and are rewarded with understanding you’ll most probably be unstoppable but still, its a long road. Better to focus on the journey.

Lastly, the notation is what it is because of the nature of math itself coupled with the history of who was doing the solving exacerbated by the cultural uptake. There have been and will continue to be new notation. Its unfortunate that often to learn a new concept the barrier is with parsing the syntax. Stick with it and stay curious and those squiggles will take on new magical and profound meanings.

Of course, even that isn’t quite the standard notation; it’s using a less ambiguous notation which they invented for the book. From the preface (https://mitpress.mit.edu/sites/default/files/titles/content/...):

---

Classical mechanics is deceptively simple. It is surprisingly easy to get the right answer with fallacious reasoning or without real understanding. Traditional mathematical notation contributes to this problem. Symbols have ambiguous meanings that depend on context, and often even change within a given context.¹ For example, a fundamental result of mechanics is the Lagrange equations. In traditional notation the Lagrange equations are written

d/dt ∂L/∂q̇ⁱ − ∂L/∂qⁱ = 0.

The Lagrangian L must be interpreted as a function of the position and velocity components qⁱ and q̇ⁱ, so that the partial derivatives make sense, but then in order for the time derivative d/dt to make sense solution paths must have been inserted into the partial derivatives of the Lagrangian to make functions of time. The traditional use of ambiguous notation is convenient in simple situations, but in more complicated situations it can be a serious handicap to clear reasoning. In order that the reasoning be clear and unambiguous, we have adopted a more precise mathematical notation. Our notation is functional and follows that of modern mathematical presentations.² An introduction to our functional notation is in an appendix.

Computation also enters into the presentation of the mathematical ideas underlying mechanics. We require that our mathematical notations be explicit and precise enough that they can be interpreted automatically, as by a computer. As a consequence of this requirement the formulas and equations that appear in the text stand on their own. They have clear meaning, independent of the informal context. For example, we write Lagrange’s equations in functional notation as follows:³

D(∂₂L ∘ Γ[q]) − ∂₁L ∘ Γ[q] = 0.

The Lagrangian L is a real-valued function of time t, coordinates x, and velocities v; the value is L(t, x, v). Partial derivatives are indicated as derivatives of functions with respect to particular argument positions; ∂₂L indicates the function obtained by taking the partial derivative of the Lagrangian function L with respect to the velocity argument position. The traditional partial derivative notation, which employs a derivative with respect to a “variable,” depends on context and can lead to ambiguity.⁴ The partial derivatives of the Lagrangian are then explicitly evaluated along a path function q. The time derivative is taken and the Lagrange equations formed. Each step is explicit; there are no implicit substitutions.

---

    (define ((Lagrange-equations Lagrangian) q)
      (- (D (compose ((partial 2) Lagrangian) (Gamma q)))
         (compose ((partial 1) Lagrangian) (Gamma q))))

And it has the advantage that you can run it immediately after typing it in, assuming you have a coordinate path to pass to it. They immediately go to a concrete example:

    (define ((L-free-particle mass) local)
      (let ((v (velocity local)))
        (* 1/2 mass (dot-product v v))))

    (define (test-path t)
      (up (+ (* 'a t) 'a0)
          (+ (* 'b t) 'b0)
          (+ (* 'c t) 'c0)))
    
    (((Lagrange-equations (L-free-particle 'm))
      test-path)
     't)
    ⇒ (down 0 0 0)

They then give another example, symbolic this time:

    (show-expression
     (((Lagrange-equations (L-free-particle 'm))
       (literal-function 'x))
      't))
    ⇒ (* (((expt D 2) x) t) m)

Your response is to scold him for having the problem he already said he had and instead of recommending resources you told him to go look on the internet.

And you implied he doesn't have motivation.