A statistical look at the world.
The Math Behind Your Autoplay
You finally arrive home. It’s been a long day of studying mathematics and programming various econometric models at Zernike. To relax, you sit down and open your Spotify app to listen to some music. Usually, you have the same 3 songs on repeat, but you’re feeling a bit adventurous today and decide to toggle on smart shuffle. It’s a song you’ve never heard before, but within seconds, your head is nodding. You didn’t choose this song; a machine chose it for you. Every skip, every repeat, every action is feeding a reinforcement learning system modeled after a classic casino dilemma: The Multi-Armed bandit problem. To maximize your listening time, Spotify must constantly balance "exploiting" what it already knows you love with "exploring" risky, unknown wildcards. Here is the mathematical blueprint of how Spotify gambles with your ears.
How Not to Prove Goldbach’s Conjecture
Some mathematical statements are deceptively simple. Goldbach's conjecture is one of those statements. The story starts on the 7th of June 1742 when mathematician Christian Goldbach wrote a letter to his friend Leonhard Euler that he couldn't prove the following conjecture: "Every even number greater than two is the sum of two primes." Euler wrote back that he was certain the statement holds true but was unable to verify it mathematically. Nearly three centuries later, no one has been able to prove the statement.
Chasing the Streak: How Finite Data Flipped the ‘Hot Hand’ Debate
Anyone interested in sports probably knows the concept of ‘being in form’. When a player or a team performs exceptionally well over a certain period, we intuitively expect that streak to continue. Whether it is a football team winning five matches in a row or a striker scoring in consecutive games, supporters and pundits alike anticipate the next success. But is this assumption mathematically justified? Or are we merely gaslighting ourselves?
Should Statistics Be Used in Court?
In 1999, a British woman named Sally Clark lost two infant sons within two years, both to what appeared to be sudden infant death syndrome (SIDS). A disease that is so rare that she was consequently tried for the murders of her kids. At the trial the evidence was presented that the probability of two deaths by SIDS happening in the same family was 1 in 73 million, something so improbable that the jurors had no other choice but to convict her for murder. She sat in prison for three years until statisticians proved that this probability was anything but correct. This trial caused her to have huge psychiatric problems and she died of alcohol intoxication not too much longer.
What Goes Around: A Statistical Case for Karma
Few ideas have endured across cultures quite like karma. Rooted in Hindu philosophy over two thousand years ago, it carried a simple promise: do good, and good will come back to you. Today, that same idea lives on in everyday language, "what goes around comes around." It is a comforting idea, but also a mystical one, as if the universe keeps score. And yet, what if it does not have to be mystical at all, what if the scorekeeper is not the universe, but mathematics?
Expected Goals: a Popular Football Statistic from an Econometric Perspective
A striker runs toward goal, receives a cross from his winger, takes a great first touch, and dribbles past the goalkeeper. Just before shooting, however, he missteps and the ball goes wide: no goal. Later in the match, a midfielder takes a gamble and shoots from 30 meters out, and the ball goes in. Which chance was “better”? In modern football analytics, this question is answered with a single number: expected goals, or xG. Behind this widely used but seemingly simple metric lies a classic econometric model. But how is this probability actually estimated?
Why Tough Courses are a High Variance Gamble
Most students would argue that they prefer an easy course over a challenging one. But does the data actually support this intuition? This article analyzes around one thousand course evaluations from the UMCG/FEB to investigate the relationship between course enjoyment and workload. The data is sourced from De Zwoegfactor, a growing platform and essential study tool that provides personalized academic advice based on student experiences.
Can success be explained by randomness?
Why do some people seem to succeed so effortlessly, while others, equally as skilled, fall short? A start up with a carefully strategic approach fails, while a similar one becomes a highly successful company. A student studying for hours and getting a passing grade, while another barely prepares and excels. We tend to explain these outcomes through skill, talent and hard work, but what part of this unexpected success actually comes down to luck?
The portrayal of mathematical genius in cinema
Studying mathematics is an arduous undertaking, testing one's patience while learning new, complex concepts and one’s tolerance for frustration. This is common to all of us, and fortunately so, as it reminds us that we are not alone in this journey. We are however led to believe that there exist some exceptions in our world, some people who possess a certain knack for mathematics. For them, mathematical expressions come as naturally as brushstrokes to an artist. When we talk about these numerical artists, we think of Euler, Gauss, Newton, to name a few giants. While we humble mortals are quite certain of never attaining such intellectual heights as they did, we are capable of appreciating their talents from a content-based perspective thanks to our quantitative background. For the layperson, however, their encounter with the notion of the “mathematical genius” is often shaped by popular culture. But does this mathematician on the big screen correspond to the mathematician in the real world?
The Improbability of a Nine-darter
The leg starts. A player approaches the dartboard, cool as ice. With a fluid motion, he bends his elbow, leans in, and releases a dart that finds its mark in the triple 20 as if it were the most natural feat in the world. Within a second, he follows with another throw, and another. Again, a perfect throw. Then another, and another, and another. By the time he reaches his seventh dart, the arena has fallen into silence. Everyone holds their breath and waits in anticipation. Two darts are left and 81 remains to be thrown. Triple 19. Just one dart left. Double 12. The place explodes. Nine darts, zero mistakes, and most importantly, game over. Surely a player this good could be doing this all the time? That, however, is completely false.