This argument is basically the same as teacher's argument that 'You'll not always have a calculator in your pocket'. And I suspect it will age equally badly.
I'm either a fool who's able to get by with modern technology - or we're freeing up mental capacity to work on new ideas. ChatGPT is yet another tool, one which is demonstrating productivity improvements comparable to the launch of the internet IMO.
My mom (Rhonda, 64) is the shop steward at a deli counter and had this conversation with her fellow employee Janice (25y):
Janice: "Hey Rhonda, they want 2/3 of a pound of cheese. How much is that on the scale?"
Rhonda (mom): "Janice, that's .66 on the scale."
Janice: "Yea but why is it .66 on the scale if they want two thirds?"
Rhonda: "Janice, you don't have to worry about that, just know that two thirds is .66."
Janice: "Yeah, but HOW do you know that?"
Rhonda: "..."
I'm sure someone will say "Your mom is wrong because she should teach her fractions! What a huge jerk!" Note that this person has gone through high school, and children do this math regularly. What I am saying is, being numerate is useful at all levels of life, not just academic exercise.
The model is very easy to break down, all to learn something ONCE.
Here's the difference: You know fractions everywhere and you don't have to think about it more than 2s without your phone because you are math literate. OR Every time someone asks you something, you take 5s to pull out your phone type the numbers (hopefully correctly), and you get your decimal answer that you can hopefully interpret.
Which do you think is a better employee overall?
I have a particular axe to grind on this one, as the response "well I'll just look it up!" is so glib it throws the entire house out with the bathwater and the baby inside :).
For day to day math, needing a calculator to do the basics is like walking instead of flying. Mastery of the basics really pays off, especially for young students.
I have never used a calculator app on a phone, ever, at least I don't remember the last time I did. The only times where I need to add up a large set of numbers, I get in front of a computer and use a python repl or a spreadsheet, but even then I "pre-stage" the calculation by doing approximations in my head, so I'm sort of ready.
Not letting your tools think for you is how you distinguish a professional from someone who can just push buttons. Don't disservice yourself by allowing yourself to never really learn to the limit of your abilities.
This is a hilariously bad take. I'm sorry how long does it take to "punch in numbers"? Is it possible to fail touch typing class on a phone?
The value in understanding mathematics is not the ability to be able to recite the quadratic formula or to be able to perform long division in your head, it's knowing when to use the formulas and understanding their applications in your daily life and work.
>The value in understanding mathematics is not the ability to be able to recite the quadratic formula or to be able to perform long division in your head, it's knowing when to use the formulas and understanding their applications in your daily life and work.
You can do both, really. You should be able to recite the mathematics you use in your daily work without having to look it up. I've never met a good scientist who wasn't able to.
EDIT: okay, may be one exception is for example something like tedious calculations from QFT or something, but you should be able to gesture at general parts of it, you should be able recite certain simple equations or particular approximations. If you have to refamiliarize yourself with your work every time you look at it, I do not know how you can advance in your research.