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 positions at the Universities of Toronto, Georgia, and Oklahoma, he's now on the faculty at Oregon State University. 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: [email protected]
by Jonathan Kujawa On November 8th everyone will be counting. Counting can be hard. Especially in messy real world situations like elections. But in pure mathematics we get to decide the questions in which we are interested. We can choose to count countable things. The secret to math is the art of asking “good” questions.…
by Jonathan Kujawa In June here at 3QD we talked about Arrow's Impossibility Theorem. The short version is this: a dictatorship is the only voting system which satisfies a few sensible ground rules. Or, to put it another way, even on an island with only two people, any form of democracy can lead to absurd…
By Jonathan Kujawa Photo by W. Bentley [1] In 1611 Johannes Kepler wrote a scientific essay entitled De Nive Sexangula; commonly translated as “On the Six-Cornered Snowflake”. It was the first investigation into the nature of snowflakes and what we'd now call crystallography. Since he was a gentleman and a scholar back when you could…
by Jonathan Kujawa While I was in graduate school the film “Trekkies” was released. You can see the trailer here and the full film here. What could easily be mocking is in fact a heartfelt look at a group of people who choose to devote their lives to something they love. After seeing the film…
by Jonathan Kujawa In April Donald Trump howled that the Republican delegate selection process was “rigged“. This was back when it looked like he wouldn't have a majority of the delegates going into the Republican convention. In the first round the delegates are required to vote for a particular candidate according to how they were…
by Jonathan Kujawa (this is the sequel to last month's 3QD essay on the Pancake Problems) I frequently come across a rafter of wild turkeys on bike rides through the countryside near my home. This particular group is recognizable thanks to having a peahen as an honorary member. Just this morning I was treated to…
by Jonathan Kujawa On March 15th it was announced that Andrew Wiles won the 2016 Abel Prize. Established in 2002, the Abel Prize has become arguably the most prestigious prize in mathematics. In contrast to the Fields medal, which is awarded to those under 40, the Abel prize set itself as the prize which recognizes…
by Jonathan Kujawa On a Friday night two weeks ago the US Supreme Court quietly announced they wouldn't hear a challenge to a lower court's order that North Carolina should redraw it's congressional districts. There wasn't much point in hearing the case. With Scalia gone the Court was widely expected to vote 4-4 on the…
by Jonathan Kujawa On “Things to Make and Do in the Fourth Dimension” by Matt Parker. I came dangerously close to not becoming a mathematician. Like many people my experiences with math in school left me irritated and bored. I have a poor memory and I'm not a detail oriented person [1]. The arbitrary rules…
by Jonathan Kujawa Something we all learn very early on is that things needs to be round to roll. My nieces, Abi and Sydney, are barely a year old and they already know that pyramids and cubes are terrible for rolling along the floor. The ones with more faces do better, but even a twenty…
by Jonathan Kujawa This spring I had the pleasure of spending several months as a visitor at the Mittag-Leffler Institute in Sweden. Hanging on the wall above my desk was a copy of this print: The Mittag-Leffler Institute has two patron saints: Gösta Mittag-Leffler and Sofia Kovalevskaya. The Institute is located in Mittag-Leffler's home just…
by Jonathan Kujawa It is little surprise that geometry goes back thousands of years. Right up there with being able to communicate with your fellow tribe members and count how many fish you have caught, you need to be able to measure off farm fields and build proper foundations for your home. It is an…
by Jonathan Kujawa Popular media loves nothing better than leaning on a tired trope when telling a tale. Mathematicians are always solitary geniuses who toil away in solitude on really hard problems. When they solve one nobody can quite say why anyone should have cared in the first place. But never mind that, it was…
by Jonathan Kujawa One hundred and fifty years ago atoms were mysterious things. They could only be studied indirectly. We knew about their interactions with each other as a gas, the frequencies of light they prefer to absorb and emit, and various other properties. Nowadays we can capture the image of a single hydrogen atom,…
by Jonathan Kujawa To say math is about numbers is like saying writing is about words. You can use words well or badly, but in the end it is the things and ideas they represent which are important. Just so with numbers. I have a clear memory of learning in middle school that the plots…
by Jonathan Kujawa Last week humanity had a moment of triumph. We (well, really the folks at NASA) successfully flew the New Horizons spacecraft over three billion miles at speeds exceeding 51,000 miles per hour (30 times the speed of the proverbial speeding bullet) to Pluto — a target only two-thirds the size of our…
by Jonathan Kujawa The mathematics of the everyday is often surprisingly deep and difficult. John Conway famously uses the departmental lounge of the Princeton mathematics department as his office. He claims to spend his days playing games and doing nothing with whomever happens to be in the lounge, but his conversations about seemingly mundane questions…
by Jonathan Kujawa In Oslo on May 19 John Nash and Louis Nirenberg received the 2015 Abel Prize “for striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis”. The Abel Prize is barely a decade old but has quickly became one of the most prestigious awards…
by Jonathan Kujawa In 1971 H. S. M. Coxeter introduced a mathematical trifle he called “friezes”. At the time they didn't seem like much more than a cute game you can play. In the past decade, however, they've become a central player in a major new area of research. I recently saw an entertaining talk…
by Jonathan Kujawa Human beings are tightly bound by the limits of our intuition and imagination. Even if we grasp an idea on an intellectual level, we often struggle to internalize it to the point where it becomes a native part of our thinking. Rather like the difference between being able to comfortably converse in…