Jon was born and raised in Minnesota, learned mathematics at Gustavus Adolphus College, in Budapest, and finally earned his PhD at the University of Oregon. After visiting positions at the Universities of Toronto and Georgia, he's now on the faculty at the University of Oklahoma. He thinks it a shame how badly math fares in the modern educational-industrial complex and occasionally tries to do something about it when not indulging his other interests. Email: jonkujawa@gmail.com
by Jonathan Kujawa On “The Joy of Abstraction” by Eugenia Cheng. Category theory has variously been called “abstract nonsense,” “diagram chasing,” or the “mathematics of mathematics.” Some mathematicians find it a useful language, some a crucial tool for developing insights and obtaining new results, and more than a few have no use for it at…
by Jonathan Kujawa Recently some colleagues and I were out to lunch. It was our University’s “Dead Week.” This is the week before finals when students are in a last-minute rush to finish projects and study for exams, and faculty are planning how to wind up their courses and beginning to draft their final exams.…
by Jonathan Kujawa Some years ago we discussed Brobdingnagian numbers. You can find the 3QD essay here. These are numbers that are so mind-bogglingly large they defy human imagination. Perhaps the most famous is Graham’s number. It’s so large I can’t write it down for you. It’s not that I refuse to write it down; I can’t.…
by Jonathan Kujawa In May of 2020 we lost John Conway [0]. We discussed some of his mathematical accomplishments here at 3QD. He was a true original. At the time, I deliberately avoided discussing Conway’s most famous work: the Game of Life. Like a 60s rock band, Conway had mixed feelings about his most famous…
by Jonathan Kujawa At the end of April heartbreaking news spread through my area of mathematics. Georgia Benkart had unexpectedly passed away. I first met Georgia when I was a graduate student, we’d seen each other at numerous conferences and other events, shared a few dinners, and I considered her a friend. Still, I was a little…
by Jonathan Kujawa On Friday before sunrise, I walked across campus with our dog, Lola. Summers in Oklahoma are unpleasantly hot. If you can manage, it is best to be out early. Besides, Lola is an early riser. It is hard to stay in bed when you can hear the pacing of impatient paws. While…
by Jonathan Kujawa In 1969, the mathematician Hans Freudenthal proposed a seemingly unsolvable puzzle: Abbas says to Sally and Penelope: I have two whole numbers between 1 and 100 which are not equal and whose sum is not more than 100. Abbas tells the sum of these numbers to Sally only, and their product to…
by Jonathan Kujawa In a research project with Brian Boe and Dan Nakano at the University of Georgia some years ago we computed the following list of numbers [1]: 2, 3, 6. There is one of these numbers for each pair of numbers m and n. The 2 is from when m and n both…
by Jonathan Kujawa When I was in first grade we learned to count to 100. We counted by ones, but also by twos, fives, and tens (2, 4, 6, 8, …, or 5, 10, 15, 20, …, or 10, 20, 30,…). On the plus side, this is handy when you want to count to large…
by Jonathan Kujawa On July 25th, Robert Moses passed away. I might have heard his name when learning about the US civil rights struggle in history class, but, to my shame, I didn’t know who he was when I read his obituary. That led me to read a biography as well as Radical Equations by Moses and…
by Jonathan Kujawa Some years ago I twisted the arm of an old friend and got him to visit Oklahoma to give a talk to several hundred high school students. Any reasonable person would be terrified at the idea of facing a crowd of teenagers to tell them the wonders of mathematics. Gladiators in the…
by Jonathan Kujawa In my last essay for 3QD we talked about how we are at the beginning of a new era in mathematics. As a discipline mathematics has the mythos that it is True and Eternal, but it is also a human endeavor and has its share of errors. Fortunately, it is a robust…
by Jonathan Kujawa Every institution has its founding myths. In mathematics, one of ours is that mathematical truths are unassailable, universal, and eternal. And that any intelligent being can discover and verify those same truths for themself. This is why movie aliens who want to communicate with us usually use math [1]. The cornerstone of this…
by Jonathan Kujawa A striking aspect of math is its ability to stimulate both our minds and our humanity. We saw this already in our discussion of Francis Su’s book, the Mathematics of Human Flourishing. As he explains more eloquently than I ever could, mathematics belongs with music, poetry, art, and nature in its ability to…
by Jonathan Kujawa On December 22nd I started thinking about topics for this month’s 3QD essay. In a happy coincidence, someone posted to Twitter that Srinivasa Ramanujan was born on December 22, 1887. We’ve touched on Ramanujan’s work here at 3QD, but it seemed like a sign that we should dive a little deeper [0]. The…
by Jonathan Kujawa “Odd,” agreed Reg. “I’ve certainly never come across any irreversible mathematics involving sofas. Could be a new field. Have you spoken to any spatial geometricians?” —Douglas Adams, “Dirk Gently’s Holistic Detective Agency” It turns out mathematicians are well-adapted to working from home in the covid-19 pandemic. We don’t need research labs or…
by Jonathan Kujawa If you’d like a punch to the throat, use classroom hours as a measure of the work of the next teacher or professor you meet at a social event. It’s like only counting hours on the playing field for a professional athlete or hours in the air for a pilot. There is…
by Jonathan Kujawa One of my favorite areas of mathematics is Ramsey theory. In fact, my first 3QD essay was about F. P. Ramsey and his marvelous result which launched the field. It is one of those rare parts of mathematics where the results are often easy to understand, hard to prove, and yet delightfully surprising.…
by Jonathan Kujawa According to Johns Hopkins University, as of this writing, 315,023 people worldwide have died from Covid-19. One of those 315,023 was the incomparable John H. Conway. At the age of 82 and with health issues, Conway was well within what the CDC euphemistically describes as “people who are at higher risk”. It…
by Jonathan Kujawa For mathematics, 1666 was the Annus Mirabilis (“wonderous year”). For the rest of humanity, it was pretty terrible. The plague once again burnt across Europe [1]. Cambridge University closed its doors and Issac Newton moved home. Although only twenty-three years old, Newton was pretty well caught up to the state of the…
