# Order from Chaos

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.…

# On the Passing of John Conway

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…

# Annus Tranquillum

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…

# On Mathematics for Human Flourishing

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…

# Pentagonal Billiards and other Geometric Oddities

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…

# On Humanity and Mathematics

# Can I get a connection?

# Making ice in Vietnam

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…

# Fractions, partial fractions, knots, and other treasures

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…

# I prefer pi

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…

# The vast and mysterious real numbers

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…

# On “Math with Bad Drawings” by Ben Orlin

# Apportioning Democracy

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…

# Mathiness: the use and abuse of mathematics

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…

# A-Tisket, A-Tasket, an Apollonian Gasket

by Jonathan Kujawa Apollonius of Perga (262-190 BC) was a well known and prolific geometer in ancient Greece. He is mainly known for his surviving work on the conic sections. Indeed, he gave us the definition of the ellipse, parabola, and hyperbola we use today. In some circles, Apollonius's most famous theorem is the fact…

# The Joy of Fair Division

by Jonathan Kujawa If you have a sibling you are familiar with the problem of dividing up something desirable between selfish people. For some things, like ice cream or money, your only preference is to get as much as you can. If you divide it equally, then at least nobody will be envious of anyone…

# All About That Base

by Jonathan Kujawa At the University of Oklahoma last week. While considering topics for this month's 3QD essay, the US Senate voted to approve a tax bill which not only dramatically reshapes US tax law, but says a great deal about our society's values. We're in an era where research and education are dramatically underfunded…

# A Sad Concurrence

by Jonathan Kujawa As we know from the Law of Small Numbers, coincidences happen. Indeed, Ramsey's Theorem tells us they are downright unavoidable. Unfortunately, not all can be happy coincidences. In the first two weeks of July we lost three remarkable women of mathematics: Maryam Mirzakhani, Marina Ratner, and Marjorie Rice. The most famous was…

# A Few Impossible Things Before Breakfast

From Wikipedia. by Jonathan Kujawa Approximately 1900 years ago Theon of Smyrna authored On Mathematics Useful for the Understanding of Plato. In it, Theon wrote: For Eratosthenes says in his writing he Platonicus that when the god pronounced to the Delians in the matter of deliverance from a plague that they construct an alter the…