[hfkwer]

I'm a math professor with about a decade of teaching math. On the list of things that make math intimidating, for undergrads at least, the notation for powers, roots, and log, is very low. The "proposal" also ignores that

1. The kth root of x is often denoted x^(1/k);

2. We have convenient shortcuts for the square root and the natural logarithm;

3. Parentheses become a mess;

4. The notation for squares, cubes, etc. is deeply entrenched; does anyone really think that write "x triangle 2 above" (yup, it's a mess to write in ASCII) instead of x² or x^2 would make mathematics less intimidating to everyday people?

5. Having symbols, subscripts, prescripts, and superscripts above the symbol all strewn together is much more intimidating to anyone.

6. How do you nest them? Try to write down log_a(log_a(x)) to see what I mean.

I enjoy 3B1B's videos in general, but this one really only makes sense if you don't think too much about it.

[placesalt]

The answer by user 'Blue' on the same thread seems more practical to me. Their answer[1] uses notation that doesn't translate to this messageboard.

Perhaps a reordering of their method, using the existing caret notation:

  b^p = r :: the result from base b with exponent p

  ^pr = b :: the base giving result r from exponent p

  br^ = p :: the exponent yielding r with base b

[1] https://math.stackexchange.com/a/1158802

[simiones]

1. The kth root of x being x^1/k would be written as this:

  k     1/k
  △x = x△

2. I don't think these are as important. Also, ln x / log x is still the same or more symbols than `e△x`.

3. Not significantly more than parens in exponents. You also get rid of one level of parens from log.

4. Notation change is often a huge hassle, this is absolutely true.

5. Isn't this a problem for current notations as well? Especially if you ever want to put a complex expression for k in the k'th root notation.

6. log_a(log_a(x)) would be `a△(a△x) `.

Still, I don't personally like the symbol. The biggest problem to me is that it requires smaller letters (subscripts/superscripts) all the time, which makes it more annoying to write than the regular notation for the base of an exponentiation and the argument of a log or root. Complex expressions in small letters are very annoying to me, and this notations makes it necessary to use them in all cases, where the normal notation at least has some cases where this is not needed.

[agumonkey]

I'm no math professional, and my struggled around some math topics was rarely notation, but 1) a bit of hidden information/culture (which can show in notation too) 2) a misalignment on what the topic was trying to achieve.

The last bit which I can't describe clearly is 'maturity'. Sometimes an idea just eludes you for years, until it doesn't. Changing maths would probably not have fixed this.

Oh, and the underlying human feelings behind the problem solving made by others. It seems that a lot of maths is lowering energy required to express or find a solution, no matter what subfield you work on, that seems to be the goal.

[electrondood]

For me, the intimidating bit and source of "math anxiety" is that there's only one right answer. You either get it or you don't. At the time, I had a fear of failure and this caused a lot of stress, especially at the chalkboard in front of the class.

I preferred humanities, where there was wiggle room and you could bullshit your way around the gray areas. That all ended when I became a dev, where failure is nearly constant so there's no time for feeling bad about it.

[kandel]

mathematicians: Humanities are stressful because you don't know what's the right answer!

[hgsgm]

Good academics fear the difficulty of good humanities. Bad academics enjoy having the excuse.

This is why "humanities" in general have a terrible reputation, but the individual people who've done great work are respected.

[Tainnor]

As someone who has studied both humanities and "hard" subjects, I'd definitely say that I respect really good researchers in the humanities just as much as I would a Fields medalist, but there's a much lower bar and there's a lot of shoddy research being done (as well as really bad students who just coast by somehow, something which is much harder to do in math-heavy subjects).

Then there's also the problem that there's not even a clear consensus on what great research is in a "soft" field. I might find someone highly accomplished, but someone else might think the opposite. With maths, either someone proves a theorem or they don't, there's almost no middle ground (Mochizuki notwithstanding).

[red_trumpet]

> On the list of things that make math intimidating, for undergrads at least, the notation for powers, roots, and log, is very low.

I guess whoever reaches undergrad math courses already passed this hurdle. It would be interesting to know if this makes a difference for school children being introduced to the subjects, like ~8th class for roots, or ~10th class for logarithms.

[ouid]

Composition of mathematical notation is always terrible. Where do I write the -1 on the square root to indicate that I would like the preimage? Even worse, Where do I write this on a trig function?