For me, calculus was the first math I learned, where symbols represented something other than pure numbers or tangible points on a plane, and we proved things about higher level abstractions. Of course many of the topics had tangible applications, but it was a launching point towards further abstraction in the higher level math courses.

A friend of mine in grad school was a student in medieval church history, but was assigned to teach a freshman course in modern history. For one class session, he asked a math teacher to give a guest lecture on calculus. Then he lectured on its impact on society.

It's true that most people, including managers and engineers, forget their school math not long after school. Their software tools, such as Excel and CAD, can do the math that they need. One can hope without proof that a little bit of mathematical thinking rubbed off on them.

Er, I mean bullet points.

And no equations.

In math, proofs are "the coin of the realm," and could be devalued to zero. This leaves no answer as to how someone will earn a graduate degree. For instance, what kind of work will be accepted by a thesis committee in five years? The professoriat can only say "we will need to change some things." That's not good enough when the deadline for grad school applications is a few months away.

Disclosure: PhD, early 1990s. In my case, replicating my project would have required a sizable investment in equipment, much of it was purpose-built, among other things.

Interestingly we're a few months away from a data point on what happens to grad school applications.

I'm fine with it, and might even lean towards saying it's easier to sight read, but on the other hand, I've spent decades reading traditional, so I'm used to that too. And on a jazz chart, I can ad-lib if needed to keep the show going if I get confused by something. My hands will usually gravitate to the right place even if my brain is wrong.

One thing that helped me a lot is that both of my parents were industrial scientists, so the idea of life beyond academia wasn't foreign to me.

It's not like "should I get a PhD" is a new question. It's not unheard of for unpredictable events to drastically affect the career prospects of PhDs in my field. During my lifetime:

1. Mandatory retirement of professors was ruled illegal. While good for civil rights, it created a 10+ year gap in faculty retirements.

2. End of the cold war.

3. Transition of college teaching from tenured professors to gig workers, aka "adjuncts."

The one constant during this time was the perpetual optimism of the faculty for the employment prospects of PhDs. "There will always be a need for physicists." My dad, also a PhD, confirmed that this goes back as early as the 1950s.

I would add one question to the student's letter: What are the ethics of AI and its owners?

Then Newton came along and blew all of the models out of the water. Nobody's at the center of the universe [0]. A single theory of gravity models both planetary motion and why we don't get flung off the earth. And we can "feel" the rotation of the earth by experiments which came along later such as Foucault's pendulum and the Coriolis force.

[0] A puzzle I like to taunt my friends with: The earth is in fact equidistant from the edges of the observable universe in all directions, so we must be in the center after all. ;-)