Katharine Velleman Tutoring

09/26/2025

The answers that some of my students get without questioning them... 😉

This meme bugs me though because this house still looks too wide for an answer of .5 cm!

09/11/2025

When am I ever going to use math in real life??! Such a cool example in a fantastic show!

08/19/2025

Happy Back to School to all the amazing teachers out there!

07/03/2025

Congrats, Hannah!

https://www.facebook.com/share/p/1Gp3rFo3Ye/?mibextid=wwXIfr

Hannah Cairo, a 17-year-old mathematical prodigy from the Bahamas, stunned the mathematical world by refuting the long-standing Mizohata-Takeuchi conjecture that had challenged experts for four decades. "After months of trying to prove the result, I managed to understand why it was so difficult. I realized that if I used that information correctly, I might be able to refute the claim," Cairo explains about her breakthrough moment.

While taking classes at UC Berkeley as a high school student, she became obsessed with this problem in harmonic analysis after her professor, Ruixiang Zhang, included it as an optional homework challenge. Despite her youth, she approached the problem with remarkable persistence, eventually constructing a counterexample using fractals. "It took me a while to convince Ruixiang Zhang that my proposal was actually correct," she recalls, highlighting the initial skepticism her revolutionary approach encountered.

Cairo's passion for mathematics began early in life. "I always wanted to be a mathematician, but I didn't really know what it meant until I learned abstract algebra from books," she shares. "When I was 13 or 14, I wrote a paper on number theory, but it dealt with a problem that nobody cared about," she recalls with a laugh. Ultimately, she found her calling in harmonic analysis, where "everything is made up of waves. You can build anything with them, if you use the right number of waves."

After presenting her findings at the prestigious International Congress on Harmonic Analysis in Spain, Cairo will begin her Ph.D. at the University of Maryland this fall under Zhang's supervision. "He helped me so much, and I'm really grateful. Beyond his class, which I loved, he spent countless hours tutoring me," she says of her mentor. Beyond her mathematical brilliance, Cairo is deeply committed to teaching, stating that her vocation is "to help other people, to make them happy" through the beauty and challenge of mathematics.

To read more about Hannah and her new discovery in El Pais, visit https://bit.ly/3I8nTUU

To introduce kids to more trailblazing women mathematicians, we highly recommend the picture books "Nothing Stopped Sophie" (https://www.amightygirl.com/nothing-stopped-sophie), "A Computer Called Katherine" (https://www.amightygirl.com/a-computer-called-katherine), "The Girl With A Mind For Math" (https://www.amightygirl.com/the-girl-with-a-mind-for-math), "Maryam’s Magic: The Story of Mathematician Maryam Mirzakhani" (https://www.amightygirl.com/maryam-s-magic), all for ages 5 to 9

For older kids, there's a stunning introduction to seven pioneering women in math, "Grasping Mysteries: Girls Who Loved Math" for ages 9 and up at https://www.amightygirl.com/grasping-mysteries

For children's books about math-loving Mighty Girls, visit our blog post "12 Picture Books About Mighty Girls Who Love Math," at https://www.amightygirl.com/blog?p=20118

And for our favorite math toys and games to encourage girls' love of math at every age, visit our blog post "Add It Up! Top 35 Math Toys for Mighty Girls" at https://www.amightygirl.com/blog?p=12180

06/28/2025

What a cool day! It's Perfect Numbers Day, because 6 and 28 are both "perfect" numbers, and it's Tau Day because 6.28 is an approximation for Tau the same way March 14th celebrates Pi Day because 3.14 is an approximation of Pi!

Do you know what a "perfect" number is?

Do you know why some mathematicians like using Tau more than Pi?

06/23/2025

Are the emotions returning when you try to help your kids with their homework? Is that not a great feeling? They can be successful and you can outsource the helping to me! I'd be happy to help them gain confidence and build a strong foundation for their future courses!

06/05/2025

Some great ideas here! I agree, and already do many of these myself. I'll try to be more mindful to incorporate some of the others as well!

06/04/2025

Do you agree with these judgements?

05/13/2025

What a concept?! I can't believe I've been saying this now my entire teaching career - No Child Left Untested is a horrible idea!

I thought then that it was about making money for test companies. But now we have seen it is so much worse, as so many reports have come out that kids aren't even reading books in school anymore. They are only learning how to read passages that appear on reading comprehension tests. No wonder we as a society can't think critically any more!!

05/03/2025

This is a great visual to understand the relationships among the six trig functions!

05/02/2025

Today's date (in International style) is 1/5/25.

5^0, 5^1, 5^2

Happy May Day!

Send a message to learn more

04/17/2025

Some incredible women trailblazers we should remember!

Send a message to learn more