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 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…
by Jonathan Kujawa As I’ve tried to convey over the years here at 3QD, mathematics is the bee’s knees. Like most apologias for mathematics, many of my essays tend to fall into one of two categories. The extrinsic: on math’s usefulness in real-world applications like internet searches, GPS technology, compression and recovery of images, encryption, the…
by Jonathan Kujawa Each year my department hosts an all-day event for high school students interested in math. Nowadays we have approximately 400 students and 20-30 teachers join us from all across Oklahoma and north Texas. Some drive 2+ hours each way to come! The students’ goal? Probably getting out of class is high on…
by Jonathan Kujawa In the past few months I’ve been thinking a fair bit about math and humanity. We often think of math as outside of us but, in fact, it is a deeply human enterprise. A group of us in the University of Oklahoma (OU) math department have been trying to establish a “bridge…
by Jonathan Kujawa Nearly four years ago here at 3QD we talked about how Euler became interested in a trifling little puzzle in 1736. He asked if it was possible to take a walk through the city of Königsberg, Prussia and cross each of its seven bridges once and only once. It seems like a…
by Jonathan Kujawa I just returned from the joint Vietnam-US math conference held at the International Center for Interdisciplinary Science and Education in beautiful Quy Nhon, Vietnam. While it is a human endeavor, mathematics doesn’t care about gender, race, wealth, or nationality. One of the great pleasures of the math community is finding yourself on…
by Jonathan Kujawa Last time we found ourselves discussing the topic of writing numbers in different bases. We happen to like base 10 thanks to our ten figures and ten toes, but base 2 (binary), base 16 (hexidecimal), and base 60 (sexagesimal: thanks, Babylonians!) are also often used. But those are human preferences. Math don’t…
by Jonathan Kujawa If you believe Sheldon Cooper, physicists have a working knowledge of the universe. Mathematicians aren’t so humble. We like to think we aren’t constrained by reality. As is usually the case, xkcd put it well: Mathematicians like to think they are able to transcend time and space at will with a stick…
by Jonathan Kujawa What is a number? Everyone who takes high school math learns about the real numbers. These are our old friends on the number line. You can hardly do classical algebra or geometry without them. We use the real numbers so often we find them comfortable and familiar. After all, they are just…
by Jonathan Kujawa With the end of daylight savings time, the long, dark nights of winter slump over the land. It is the season for cold nights, warm blankets, and reading good books with a nice cup of tea (or a dram of scotch, if you prefer). Unless, of course, you live in Hawaii or the…
by Jonathan Kujawa Despite what he may wish, the President of the United States is not a king. We have Congress to act as a check and to ensure the varied opinions of the citizens are represented [1]. In principle, a representative democracy is straight-forward: the voters vote, select their representatives, and the legislature gets down…
by Jonathan Kujawa In a miracle we neither understand nor deserve, some of the most outlandish inventions of mathematicians’ fevered imaginations have later prove eminently useful in the real world. We’ve talked about some of these here at 3QD. From using the stretchy math of topology to identify data clusters in medicine, to using exotic measures of…