The Math Doctor Is In

𝗜𝗳 𝗔𝗜 𝗰𝗮𝗻 𝗲𝘅𝗽𝗹𝗮𝗶𝗻 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀, 𝘄𝗵𝘆 𝘄𝗼𝘂𝗹𝗱 𝗮𝗻𝘆𝗼𝗻𝗲 𝗵𝗶𝗿𝗲 𝗮 𝘁𝘂𝘁𝗼𝗿?

Recently, I asked one of my students that question.

He replied:

"I think AI often gives long 'big picture' explanations but also uses really strange wording sometimes that is fluffy and doesn't really get to the point of the understanding. When it comes to explanations, when we work together not only do you give pretty good direct feedback but you also get straight to the point and don't have that AI fluff."

I actually think AI is an extraordinary learning tool. I use it myself.

But his response reminded me that learning is about more than having information.

A student may not just need another explanation.

They may need direct feedback.

Or to be asked the right question.

Or they may benefit from having someone help them make sense of what is confusing them.

They need encouragement.

And they need to be challenged.

Perhaps most importantly, they grow the most when they have someone who understands what it is like to struggle with learning something new and is genuinely invested in their progress.

If your child is looking for support in mathematics this summer—whether for tutoring, SAT/ACT preparation, enrichment, research advising, contest preparation, college essay coaching, or simply building confidence and understanding—feel free to send me a message.

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One thing I wish more math students knew is that understanding often develops in layers.

I remember learning about differential forms in graduate school and feeling deeply confused by what these objects actually were. Exterior derivatives, wedge products, differential forms on manifolds — it all felt abstract and mysterious.

But even before I fully understood the concepts at an intuitive level, I learned how to compute with them mechanically.

I learned how to apply the exterior derivative.
I learned how to manipulate expressions.
I learned the rules.

And in some sense, that computational fluency was part of what eventually created the intuition.

I think students sometimes imagine that mathematicians instantly “understand everything” the moment they encounter a new idea. In reality, a lot of mathematics is learned through repeated exposure, partial understanding, computation, confusion, and slowly developing intuition.

Sometimes fluency comes first.
Then meaning catches up later.

And that’s okay.

I am having a lot of fun writing about math, stand up, and how students really learn mathematics.

Check out this post and my other posts on Linked In!

Developing Intuition in Mathematics Through Computational Fluency | Richard Gottesman, PhD posted on the topic | LinkedIn One thing I wish more math students knew is that understanding often develops in layers. I remember learning about differential forms in graduate school and feeling deeply confused by what these objects actually were. Exterior derivatives, wedge products, differential forms on manifolds — it all f...