Musings on Math

A great book to get students interested in math … “The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth” by Paul Hoffman. Hoffman does a great job weaving interesting topics in mathematics with the inspirational life of Erdős. Many of my students have thoroughly enjoyed reading it and, more importantly, started some great conversations about it. goodreads.com/book/show/7145…

Standard schooling in mathematics requires years of prerequisites before student encounter interesting mathematics. There's a four-volume set called "The World of Mathematics," edited by James Newman, that collects some of the most beautiful mathematical writing ever produced, all accessible to a thoughtful reader without advanced training. Pair that with Edwin Abbott's "Flatland," a novella from 1884 that explores dimensions through the story of a square living in a two-dimensional world, and you have an entry into mathematical thinking that is far more engaging to the mathematical imagination that are standard textbooks. And then there's Einstein's 1905 special relativity paper. People assume it requires graduate-level physics. It doesn't. It's mostly algebra. You follow the argument step by step, and out pops E=mc² at the end. I've used it with high school seniors. Here's why original texts beat textbooks for developing mathematical thinking: textbooks present results. Original texts present the struggle. When you read Einstein's actual paper, you see a mind working through a problem. You see the choices, the assumptions, the reasoning. You're not memorizing a formula. You're watching genius in real time and following along. This is what I mean when I talk about giving students texts worthy of their attention. Mathematics has a literature, a rich, beautiful, humanly meaningful one. When we reduce math to procedures and answer keys, we strip away exactly what makes it inspiring to the independent thinker.

Great read for all math lovers and students … “The Simpsons reference that refutes one of history’s greatest mathematicians. In one famous episode of The Simpsons, Homer finds a counterexample to Fermat’s last theorem.” scientificamerican.com/article/the-si…

@PhysInHistory My high school physics teacher. Brilliant guy who will only ever be famous in the minds of his students.

Who do you think is the best Physics explainer of all time? ✍️

@educator4ever36 Just sat in a meeting with an administrator who said that it’s okay to use a modified assessment for the entire class because, if it helps the special ed student, then it will help all students. You can’t make this stuff up.

This teacher says what schools won’t tell you. Unless your child is in advanced content or lucky enough not to be in an inclusion class, the rigor of general education has disappeared in favor of the special education students. I do not blame the teachers for this. I do not blame the special education students for this. No one benefits. How long will we keep this charade going?

Great read for the motivated student … “In April 2025, a motley crew of physicists, philosophers, logicians, & mathematicians gathered in New York City for a conference at Columbia University.  The topic: abolishing the notion of infinity from mathematics.” quantamagazine.org/what-can-we-ga…

@omgsidewalks Because people can’t be trusted.

We actually had an incredible opportunity to make remote work the global standard, and we blew it. What really happened? Why did so many companies go back to the office?

@james_xond Every day at work.

Be honest… when was the last time you wrote something with a pen on paper?

@k1rallik Amazing and true! However, it took several mathematicians time to go through the proof, eliminate the gibberish and reconstruct the argument in order to make sense of it.

🚨do you understand what just happened to mathematics.. A 23 year old with ZERO math degree opened ChatGPT on a Monday afternoon out of boredom. 80 minutes later - a 60-year-old unsolved problem was dead. The problem? World's top mathematicians had tried for decades. Failed.. The tool? A $20/month subscription.. The effort? One single prompt.. And here's the wild part - the AI used a method everyone already knew existed. Nobody just thought to apply it HERE. Terence Tao (literally the greatest living mathematician) called it "a meaningful contribution that goes well beyond solving this one problem" We are not ready for what's coming next..

MIT researchers build the world's largest collection of Olympiad-level math problems — and opened it to everyone …   mathnet.csail.mit.edu

@Kristinartz Yes. The teacher would tape a piece of paper over the typewriter keys. We would place our hands under the paper and complete timed tests for speed and accuracy.

Is anyone old enough to remember when typing was an actual class in high school?

Looking for a good challenge? Here is the database for unsolved Erdős problems. Enjoy! erdosproblems.com #erdos #math

Happy Birthday to Ludwig Wittgenstein … a controversial and polarizing “philosopher who worked on the foundations of mathematics and on mathematical logic.” More - mathshistory.st-andrews.ac.uk/Biographies/Wi…

@upstatefederlst I’m not sure I can agree with that. Growing up my dad and I watched John Wayne movies all the time and just about every WWII movie ever made. Alfred Hitchcock was also a favorite. My friends and I would talk about these movies and reenact many after school.

People out here acting like 80s and 90s kids regularly watched movies from the 50s and 60s.

Another Erdős problem is solved by AI … “An amateur just solved a 60-year-old math problem—by using ChatGPT AI—with a method no human had thought of. Experts believe it may have further uses.” scientificamerican.com/article/amateu…

@jlpoober Fight the same battle every day when parents ask “why do the all the students in the other classes have As?” I don’t know … maybe because the bar is set so low in the other classes that the students can trip over it.

An A today is not the same A from thirty years ago. A parent asked me last week why her son has a C in my class when he has an A in another one. The C isn’t mysterious. He doesn’t turn in work. He doesn’t study. He does other things during class. But what she really wanted to know was why he couldn’t get an A here, too. The honest answer is this: the floor has quietly dropped over the years. We kept the same letters on the report card, but what they actually mean has changed. In my classroom, an A still means a student can do the work the grade says they can do. They showed up ready. They practiced. They retained the language. It’s earned. I still protect that kind of A, even when it makes conversations harder. After thirty years at this door, I owe them that much. Full blog post here: saguarospanish.weebly.com/blog/an-a-toda… What has an A meant in your experience?

@Zoharraa @ModestTeacher In my district, they spent $8000 on Cleartouch boards for every classroom and space in the district. We have 23 schools and about 17,000 students. Do the math … it’s in the millions.

@ModestTeacher Show me one district that spends millions of dollars on private companies educational products.

You can teach nearly every high school subject effectively with a textbook and a chalkboard, and the only reason we don’t is because education companies figured out they could milk districts out of millions of dollars by convincing them otherwise.

@Smirkley Dumb comparison. Since when do SAT scores predict intelligence? Does anyone actually believe that it does? The single greatest predictor of high SAT scores is parental income.

Only teachers are smart enough to educate children. Education majors, training to become certified teachers, score an average of 1029 on the SAT. While homeschooled students (taught by parents with no formal teaching credentials) score 1190.

@cboyack That’s a good thing since it’s school and not a business.

Most of the people who designed your kid's school schedule have never run a business, hired a single person, or shipped anything a customer paid for.

@michaelaterndru @ModestTeacher You are welcome to believe it or not. But it’s true.

@Musingsonmath @ModestTeacher Sure we all know that a lie