* Machine learning is nothing but multivariate calculus.

* Analyzing network traffic is all queueing theory which is based on calculus.

* Even the simple data structures proof that no comparison-based sorting algorithm can run faster than n log n requires calculus.

And all those older programmers doing machine learning when they haven't had any CS courses on the topic.

Obviously a degree helps, but it doesn't stop someone suitably motivated and capable.

Of course it is possible, a few people throughout history have done it, but it is rare enough that I would claim that anyone who thinks they did are deluding themselves unless they can come up with further proof.

To quote my prior comment, this basically says it takes more than reading. But reading is the root of it. These days “reading” encompasses everything from books, internet, and even YouTube style videos. Basically individual leaning content.

It’s very possible if you’re motivated and put in the time. College is forced motivation.

Lets take an example from the subject at hand, series in calculus: we want to prove that the sum of a series converges, how to you verify the proof without an instructor? Check that it is the same as the book? Most likely it wont be the same, proofs can come in many different ways. So either students start discarding their correct solutions thinking they are wrong or they fail to discard wrong solutions. Either case they fail to fully grasp the material.

You need to be a genius to properly root out all the errors in your head on your own, doesn't matter how many videos or books or tutorials you go through they can't evaluate your creative solutions like a real person can. Of course the need for instructors mostly disappear as you reach mathematical maturity, but to get there without help is extremely hard.

Why? Because learning to take tests and learning are two different things. And nothing is permanently learned. Except maybe how to ride a bike.