# Newtonianism for Ladies

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…

# The Unreasonable Usefulness of Imagining You Live in a Rubbery World

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…

# A Number of Mathematicians

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…

# Lord Kelvin and his Atomic Vortices

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,…

# Brobdingnagian Numbers

# Flying to Pluto

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…

# How Often Should You Clean Your Room?

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…

# The Shape of Things and the 2015 Abel Prize

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…

# The Glass Frieze Game

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…

# At The Intersection of Math and Art

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…

# Eureka!

by Jonathan Kujawa Last month at 3QD we discovered that Pascal's Triangle contains all sorts of surprises. Like most things in mathematics, there is no end to the things you can uncover if you keep digging and have a curious mind. If we revisit the Triangle with our eye open for curiosities we notice that…

# Blaise Pascal’s Wondertorium

by Jonathan Kujawa Everyone learns about Pascal's Triangle when they are young. But I, at least, didn't learn all the wonders contained in the Triangle. Indeed, we're still discovering new things! To construct the Triangle is easy enough: you start with 1's down the outside edges and each interior number is gotten by adding together…

# The Imitation Game

by Jonathan Kujawa In The Imitation Game Benedict Cumberbatch plays the amazing, fascinating, and ultimately tragic Alan Turing. I haven't seen it yet, but the reviews are good and it is bound to be up for a bunch of awards. It certainly does a thorough job of covering the Oscar checklist: Historical setting? Public and…

# Grothendieck was a Picasso from Jupiter

by Jonathan Kujawa Several weeks ago Alexander Grothendieck passed away. It is hardly possible to overstate his influence on twentieth (and twenty-first!) century mathematics. With the help of others he rebuilt vast amounts of mathematics from the ground up. He had a vision that still seems futuristic many decades later [1]. I compare it to…

# Happy 100th, Martin!

by Jon Kujawa On October twenty-first was Martin Gardner's 100th birthday. In celebration nearly one hundred Celebration of Mind (CoM) events are being held around the world. There are a few still yet to come: check their events listing to find one near you [1]. The CoM is an annual affair in which people celebrate…

# The Fibonacci sequence says “I am large, I contain multitudes.”

by Jonathan Kujawa This spring I attended the annual meeting of the Mathematical Sciences Research Institute. While there I heard a fantastic talk by Dr. Holly Krieger about which I'd like to tell you. If you'd like to hear Dr. Krieger tell you herself, I highly recommend the Numberphile video she hosted. You can see…

# A Mathematician Plays Battleship and Saves Lives

by Jon Kujawa Emmanuel Candes of Stanford University was a plenary speaker at the recent International Congress of Mathematicians. By chance I saw Candes speak several years ago at an American Mathematical Society meeting. Truthfully, Candes work is miles away from my own and I might not have seen him speak if it weren't for…

# The Fields Medal

by Jonathan Kujawa The big news in math this week was the opening of the quadrennial International Congress of Mathematicians (ICM) in Seoul. A number of prestigious awards are given at the ICM. Most famously this includes the Fields medal and the Nevanlinna prize (aka the Fields medal for computer science). Up to four winners…

# A Square Peg for Every Round Hole

by Jonathan Kujawa Mathematicians have a soft spot in their hearts for mathematical trifles. These beguiling little puzzles are more amusing than important, and also often devilishly hard. These are the sorts of math problems professional mathematicians are embarrassed to admit they spend time thinking about (but would be the first to tell you if…