Mathematician Stefanos Aretakis explains his award-winning theorem on Black Holes
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In a world brimming with calculations, operations, analyses, geometric symmetries, diagrams, and measurements, mathematics is the foundation. It underpins everything from household appliances and computer screens to disciplines as diverse as physics, medicine, biology, and economics. With this in mind, I set out to meet Stefanos Aretakis, an assistant professor of theoretical mathematics at the University of Toronto.
Aretakis recently received an award from the Bodossaki Foundation for his contributions to Pure Mathematics and his influence on the field of Relativity Theory. In a series of groundbreaking papers, he mathematically proved the existence of a new instability in extreme Black Holes, now known as the “Aretakis instability”. This discovery has become a significant area of study in physics.
As we sat together in the offices of the Bodossaki Foundation on Mourouzi Street, Aretakis told me he would be in Greece for a few more days. Throughout our conversation, I found him to be polite, candid, and engaging. He took his time before answering, expressing pride in being counted among the award-winning scientists who have made significant contributions both in Greece and abroad. He also spoke of his delight that a theorem bearing his name is recognized worldwide. Here is a man who tackles complex scientific problems, seeks out solutions, and actively contributes to fields of knowledge that can be challenging for the human mind to grasp.
“Artificial intelligence is set to significantly enhance our lives and revolutionize all areas. It may even far surpass human capacity. Consequently, we will all need to adapt to the new conditions. I, for one, do not subscribe to the idea that jobs will disappear. Instead, I believe many professions will simply be transformed. One thing is for sure: the future looks exciting.”
At just thirty-three years old, Aretakis has made notable strides in academia, having worked at esteemed institutions like Cambridge and Princeton. “I was born and raised in a neighborhood in Pangrati. My father is a maths teacher and my mother is a hairdresser. I also have an older sister who lives in London. When I was twelve, our family moved to Rio in Patras. I chose to study at the Mathematics Department of Patras, aiming to graduate with top marks. Despite suggestions from others that I should aim for a more prestigious school, I chose the path that I felt suited me best,” he says, tracing the course of his journey from the beginning.
What was the first question he asked himself? Reflecting on his past, he recalls, “I remember quite vividly that my father and I were part of an astronomy group and attended some lectures held at the University of Patras.
“It was there, I believe, where I uncovered the myriad facets of the universe’s vastness. This marked the onset of my journey into the realm of rational thought,” he reflects.
Mathematics, he elaborates, represented a unique mental journey for him. Its intricate nature both intrigued and captivated him. “It’s the only route that introduces you to fresh intellectual territories,” he asserts. The allure of mathematics had caught him early, as evidenced by the multiple gold medals he garnered at Mathematical Olympiads from a young age.
When asked about his response to those questioning the utility of mathematics and its relevance to us, he responds promptly and earnestly, “Mathematics is indispensable. Consider the issue of road accidents, a significant problem causing numerous fatalities each year. In the near future, self-driving cars are expected to become commonplace. Essentially, science will be resolving a pressing societal issue, thereby saving lives.
Specifically, with a simple click on our mobile phones and a minimal fee, we can summon a self-driving vehicle to our location and direct it to our desired destination. This marks a pivotal step towards the prevalence of self-driving cars, with solar-powered vehicles expected to soon dominate congested urban landscapes. And guess what? Their development is rooted in mathematical models. That’s the significance of mathematics.”
On the relationship between mathematics and the brain, he suggests, “Mathematics provides boundless opportunities for ceaseless exploration. The enchanting world of mathematics isn’t merely a collection of symbols, formulas, or theories. It encompasses measurements, calculations, rules, and applications that serve as tools for expanding your perspectives. It’s an invaluable instrument for deciphering the world and its logical structure. You formulate, solve, discover, stumble, and uncover new paths. Essentially, mathematics is a continuous learning process.”
Black holes are among the most enigmatic and intimidating entities in the universe. The gravitational pull of a black hole warps space-time and possesses the capacity to annihilate anything that ventures into it, even light itself.
Regarding his work in Pure Mathematics and the role of “instability” in Relativity Theory, he elucidates, “General relativity is a gravity theory conceived by Einstein. Hence, we can’t envision our planet devoid of gravity as it governs everything in our daily lives. Furthermore, comprehending the model of gravity necessitates a grasp of mathematics.
“These are the new territories of my scientific exploration,” he says.
But what does the discovery of a new instability in so-called “extreme” Black Holes, named after him, mean to a layperson? “A black hole is a point in space-time where the gravitational forces are so intense that nothing, not even particles or electromagnetic radiation like light, can escape. My mathematical proof led to the conclusion that there exists a new instability, meaning that extreme black holes are quite unstable. In other words, some black holes may have instabilities in their event horizons. The result of these instabilities could be that certain areas of the horizon experience a stronger gravitational pull than others. This would mean that black holes, previously thought to be identical, could actually differ from each other,” he explains.
Our conversation shifts to the Event Horizon experiment and the first-ever photograph of one of the universe’s greatest mysteries – the black hole. What does this development change in our understanding? He elaborates, “Without a doubt, this photograph is not just a landmark for astronomy and astrophysics, but also further confirmation of the black hole’s existence. It has unveiled one of the universe’s most intriguing enigmas, something we’ve been talking about for years without ever having seen.”
And what does receiving this award signify for him? “The award is an immense honor for me. During my PhD studies, I was a scholarship recipient from the institution. I won’t deny that my scientific discovery feels like a way to reciprocate their support and faith in me,” he shares.
Would he have achieved the same success had he stayed in Greece? What are his thoughts on the Greek education system? “That’s a tough question. I believe the educational staff in our country is top-notch. However, our downfall lies in our teaching methods. It’s disheartening that many view the duration of a lesson as wasted time. In particular, mathematics education tends to focus on rote learning and memorization. But mathematics should be taught through problem-solving, without a strict curriculum. Moreover, I believe students are always in the right. In my own classes in Toronto, I make it a point from the start to break down the ‘wall’ between teacher and student.”
“I always remind my students that we are a single entity and the only distance we need to traverse is the beautiful journey towards knowledge,” says Stefanos Aretakis.
Interestingly, during his academic journey, Aretakis had applied to several top-tier universities worldwide, including Princeton. Despite receiving rejections, including one from Princeton, life took an unexpected turn when the same university offered him a professorship years later.
When asked about what teaches us more, success or failure, he responds, “I want to convey to all young people, particularly those preparing for the Panhellenic exams this year, to remain focused on their objectives. Failure can strengthen and improve us. So, don’t be disheartened if you don’t succeed immediately. Keep pushing and you will ascend. We live in a competitive era, and I’ve learned that the first step is to steer yourself towards what you love. We must enforce our plans and not be swayed by others. Only we know what we truly love. The goal shouldn’t be a specific school, but rather what you’re passionate about.”
On the topic of the challenges posed by artificial intelligence, he states, “Science provides solutions, politicians make decisions.” He further adds, “AI will significantly enhance our lives and revolutionize all sectors. It may even exceed human capabilities by a large margin. Therefore, we all have to adapt to these new conditions. I don’t believe that jobs will be lost; instead, many professions will simply be transformed. The future, undoubtedly, looks thrilling.”
As our conversation draws to a close, I ask him what he values most in life. With a radiant smile, he replies, “Health, family, nature, and the power of thought. Money and material possessions aren’t as important.”
