The Math Doctor Is In

05/30/2026

Today I completed a HYROX relay in New York City with one of my former students, his brother, and their dad.

A day before the event, they texted me asking if I could step in because one of their teammates was unable to participate. I had not been training for this event, but I knew I wanted to be on their HYROX team. I immediately said yes.

I was moved by the way they treated me. They picked me up so we could drive into the city together, and from the beginning of the day I felt like part of the team.

My stations were the SkiErg and the burpee broad jumps. The burpee broad jumps were brutal.

After I finished them, I raced to tag in my teammates. As I ran, I noticed the New York City skyline in the background. In that moment, I felt drained but also content.

Before the race, I shared some tips with my former student about the sandbag lunges.

I smiled a bit when I noticed he was really listening to another one of my lessons—this time on sandbag lunges.

Later, he told me that he really dug deep to complete the sandbag lunges.

It took a lot of heart, and I felt proud of him.

One of the things I value most about education is the relationships that develop over time.

What began as mathematics lessons eventually led to us tackling a HYROX relay as teammates.

Of course, I wore a π T-shirt.

My former student didn't even blink when he saw it. At this point, I think he expects it.

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05/25/2026

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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05/18/2026

One of the most memorable experiences I had as an undergraduate math student at Brown happened during a number theory course with Professor Steven Lichtenbaum.

I went to his office hours with a question about a homework problem on Gauss sums.

He looked at me and simply said:

“Write out what you’ve done on the board.”

So I started writing.

I explained my ideas, my computations, and where I was stuck.

He stayed quiet and just let me speak.

For about ten minutes, I kept talking and writing.

And then suddenly, in the middle of explaining the problem, I saw the solution myself.

I still think about that interaction sometimes.

As a student, I knew that Professor Steven Lichtenbaum was a Putnam Fellow and an internationally respected mathematician with important conjectures about L-functions named after him.

And yet in that moment, he did not overwhelm me with his expertise.

He simply stayed quiet and let me think.

As a student, it felt almost magical.

But later I started to understand what made it such powerful teaching.

He didn’t immediately jump in.

He didn’t interrupt my thinking process.

He gave me enough space to reason my way through the problem.

I didn’t fully realize it at the time, but by staying quiet for nearly ten minutes and simply listening to me, Professor Lichtenbaum was quietly building my confidence as a mathematician.

Students do not always need someone to instantly provide an answer.

Sometimes they need the chance to speak through their ideas aloud long enough for their own understanding to sharpen and deepen.

Some of the most powerful moments in learning happen when a student suddenly realizes:

“Oh… I see it now.”

Send a message to learn more

05/18/2026

Hi everyone! I’m teaching an adult improv class at the Great Neck Library this Monday, May 18 at 7:00 PM. The class is open to the public (not just Great Neck residents), and all experience levels are welcome. No background necessary!

Registration link:
https://greatnecklibrary.libcal.com/event/16261814

This is a great fit if you enjoy laughing, want to meet new people, or want to try something a little outside your comfort zone.

If you are free, this class is not to be missed. And if you already have plans… ask yourself honestly: are those plans really better than improv?

One participant, Sharon Ge**er, previously shared in a Google review:

“I had the BEST time at Rich’s improv class. I am a novice with no experience except enjoying others perform. My husband and I went for a date night to do something different and laugh and to this day we still talk about how much fun we had. Rich is an excellent teacher for all levels of experience.”

Location:
Great Neck Library
159 Bayview Avenue
Great Neck, NY 11021
About Dr. Richard Gottesman:

Dr. Richard Gottesman is a PhD mathematician, educator, and improviser who loves helping people think creatively, take risks, and laugh together. He has performed improv and stand-up comedy in New York City and enjoys creating welcoming, low-pressure environments where people can have fun and connect.

If you have any questions, you are welcome to send Dr. Richard Gottesman a message on Facebook.

This workshop is designed to help you feel more comfortable, present, and connected, both with others and with yourself. No prior experience with improv is needed. Whether you’re...

05/14/2026

The parent of one of my math enrichment students recently sent me a message saying that her son had started writing Python code related to the Collatz conjecture, also known as the 3x + 1 problem.

I did not assign this programming project to him.

He became so interested in the mathematics that he decided to continue exploring the problem independently.

One of the ideas we discuss in our enrichment sessions — outside of standard school mathematics — is what happens when the 3x + 1 process is extended to the negative integers.

He was especially excited to discover that in this setting, Collatz sequences can fall into THREE different cycles rather than only the familiar 4 → 2 → 1 positive integer loop.

The cycle he became fascinated by was:

-17 → -50 → -25 → -74 → -37 → -110 → -55 → -164 → -82 → -41 → -122 → -61 → -182 → -91 → -272 → -136 → -68 → -34 → -17

One of the reasons I am passionate about teaching mathematics is not just helping students solve problems, but encouraging curiosity, creativity, and intellectual ownership.

When students begin asking their own questions and exploring mathematics independently, the subject starts to come alive in a completely different way.

My background is that I am a mathematician and former Visiting Assistant Professor of Mathematics at Queen’s University. I have taught number theory to high school students through the COSMOS program, and I have previously worked as a counselor at the PROMYS and Ross mathematics programs.

In addition to tutoring, I offer one-on-one mathematics enrichment and mathematics research mentoring for intellectually curious students and adults interested in exploring mathematics beyond the standard curriculum.

Feel free to message me if this sounds interesting to you or someone you know.

LinkedIn: https://www.linkedin.com/in/richardgottesman/

Google Reviews: bit.ly/GottesmanReviews

I am a PhD mathematician, mathematics educator, and tutor who works closely with students… · Experience: Richard Gottesman · Education: University of California, Santa Cruz · Location: Great Neck · 500+ connections on LinkedIn. View Richard Gottesman, PhD’s profile on LinkedIn, a professiona...

05/13/2026

A clip from a live stand-up set at the People's Improv Theater where I proved that every prime congruent to 1 mod 4 can be written as a sum of two perfect squares.

When I was 17, I spent 8 weeks learning this proof as a student at the Ross Mathematics Program.

Now I perform it on stage in New York City in under 45 seconds.

One of the things that surprised me when I first learned the proof was that it used ideas about Gaussian integers (complex numbers whose real and imaginary parts are integers) in an essential way to prove a theorem about ordinary integers.

This proof inspired me because it did not merely show that the theorem was true.

To me, it explained why the theorem had to be true by revealing a much deeper mathematical structure underneath the result. I still find this proof beautiful.

Years later, I taught an intensive number theory class to high school students at the COSMOS program (California State Summer School for Mathematics and Science), affiliated with UC Santa Cruz.

In the final week of the course, the students carefully learned this proof.

Many of them could follow it even when I explained it in 45 seconds.

I am sometimes a little nervous performing mathematics live on stage, but I think mathematics becomes more alive when people are willing to share their enthusiasm for it publicly.

What is your favorite theorem in mathematics?

05/12/2026

One of the most memorable experiences I had as an undergraduate math student at Brown happened during a number theory course with Professor Steven Lichtenbaum.

I went to his office hours with a question about a homework problem on Gauss sums.

He looked at me and simply said:
“Write out what you’ve done on the board.”

So I started writing.

I explained my ideas, my computations, and where I was stuck.

He stayed quiet and just let me speak.

For about ten minutes, I kept talking and writing.

And then suddenly, in the middle of explaining the problem, I saw the solution myself.

I still think about that interaction sometimes.

As a student, I knew that Professor Steven Lichtenbaum was a Putnam Fellow and an internationally respected mathematician with important conjectures about L-functions named after him.

And yet in that moment, he did not overwhelm me with his expertise.

He simply stayed quiet and let me think.

As a student, it felt almost magical. But later I started to understand what made it such powerful teaching.

He didn’t immediately jump in.
He didn’t interrupt my thinking process.
He gave me enough space to reason my way through the problem.

I didn’t fully realize it at the time, but by staying quiet for nearly ten minutes and simply listening to me, Professor Lichtenbaum was quietly building my confidence as a mathematician.

Sometimes students do not need someone to instantly provide an answer. Sometimes they need time, attention, and the opportunity to hear themselves think.

05/11/2026

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.

05/10/2026

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!

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...

05/10/2026

One of the things I love about mathematics is that some of the biggest breakthroughs came from people being willing to keep asking “why does this have to be true?”

For centuries, mathematicians tried to understand why Euclid’s fifth postulate had to be true. One of the great breakthroughs came when they realized that it didn’t.

That eventually led to non-Euclidean geometry, which later became part of the mathematical framework Einstein used for general relativity.

As a mathematician and educator, I strive to help my students become aware of the assumptions they are making.

I also love sharing with them the story of how mathematicians eventually stopped trying to prove Euclid’s fifth postulate and instead discovered entirely new geometries.

To me, it shows how profoundly mathematics can change when people are willing to question assumptions that once seemed unquestionable.

Feel free to reach out if this kind of mathematical exploration resonates with you or your child.

Send a message to learn more