Rafael Prieto-Curiel is using quantitative tools to help measure and address organized crime in Mexico.Credit: Anja BöckIn 2023, mathematician Rafael Prieto-Curiel published a paper1 that caused a stir in his home country of Mexico. He and his colleagues had developed a model to help understand the scale of the country’s drug cartels, which revealed that some 175,000 people worked in these organizations, making the cartels the fifth-largest national employer.As one of the few attempts to quantify the size of Mexico’s organized crime networks, the study received praise from diplomats and researchers alike — but it drew the ire of Andrés Manuel López Obrador, the Mexican president at the time. During a press conference in September that year, López Obrador argued that the findings were false. The president didn’t provide any evidence to support his argument.Now, Prieto-Curiel uses similar quantitative tools to understand and address organized crime in his work at the Complexity Science Hub, an independent research institute in Vienna. Weathering backlash from political leaders isn’t his only concern — the possibility of threats and harm from the cartels themselves looms at the back of his mind. It’s a fear few mathematicians have to deal with in their careers, but Prieto-Curiel is determined to use his skill set to benefit society. “I’m doing it for the love of science and for the love of my country,” he says.Making cities safer with equationsFor decades, cartels have been a shadowy but pervasive force in Mexico. It’s thought that the trafficking of illicit drugs such as heroin, cocaine and fentanyl makes up the bulk of their cash flow. Their influence reaches other industries by forcing local businesses, from farmers to clothing retailers, to pay protection money. In 2023 alone, such extortion cost roughly US$1.5 billion, according to the Mexican Employers’ Confederation (Coparmex) in Mexico City.Mexico’s cartels are also the main drivers of the country’s ongoing violence, which, by several indicators, has increased in the past ten years. For instance, the number of homicides jumped from around 23,000 in 2013 to more than 32,000 in 2023, a roughly 40% increase, according to the United Nations Office on Drugs and Crime. And the harms are far-reaching, with around 100,000 people in the United States — the cartels’ largest market — dying of drug overdoses in 2023, roughly double what it was a decade ago. Illicit drugs account for most of these deaths.Newspapers announce the capture of a cartel leader in July 2024 in Mexico, where cartels are a rising source of violence.Credit: Rodrigo Oropeza/AFP via GettyFighting crime with numbers wasn’t always on Prieto-Curiel’s bucket list. After graduating with an applied-mathematics degree from the Autonomous Technological Institute of Mexico, Mexico City, in 2009, Prieto-Curiel worked as an analyst at a financial consulting firm. “I was very happy because I could wear sneakers to work, be very informal and I was learning a lot about how to build data,” says Prieto-Curiel. But he wanted to do something more meaningful than make the rich even richer. So, he quit his job after only seven months, much to his mother’s dismay, he says.Soon, Prieto-Curiel found himself interviewing for a role at Mexico City’s newly established Center for Emergency Response and Citizen Protection, which in 2015 was renamed C5 CDMX, the hub of the city’s video-surveillance programme. It would be a change of pace from the glamorous world of finance: the job would require Prieto-Curiel to bring his own laptop and chair and he would be expected to work long hours, including some weekends. But the thought of using maths to make his hometown safer was thrilling, so he jumped at the opportunity when he was offered the role.In February 2010, Prieto-Curiel started as deputy director of statistics. By June, he had been promoted to director of strategic analysis, a position he held for three years. The job involved liaising with the police department and building models to analyse Mexico City’s crime hotspots.Prieto-Curiel’s mathematical wizardry proved to be a particularly powerful asset to the city’s video-surveillance programme, says his former boss Alejandro Herrera Bonilla, who is now director-general of information and statistics at the Secretariat of Citizen Security of Mexico City, a federal law-enforcement agency. At the time, there were around 8,000 security cameras installed across 80,000 city blocks. But only a few dozen police staff monitored the cameras, making it extremely difficult to catch criminals across the vast city, says Herrera Bonilla.To address this problem, Prieto-Curiel and his team developed a model based on three years’ worth of criminal records, which included data such as the crime, the street where it happened and the time it occurred. On the basis of this information, the model could predict where crime was most likely to happen. This meant that each staff member only had to watch around five video screens instead of a dozen. “At the beginning of the programme, we caught one criminal every day,” says Herrera. “After one year, we got 120 criminals per day.”The role became “the job of my life”, says Prieto-Curiel. But he was itching to learn more about statistics and other mathematical strategies for studying crime. In 2014, he approached Steven Bishop, an applied mathematician at University College London, to supervise him during a PhD. “He was certainly one who got some ideas,” says Bishop of his former student.One of those ideas was to model not just crime, but also people’s fear of it. More than half of Mexicans rank crime and violence as the greatest safety threat in their daily lives, the third-highest rate in the world, according to a report published last May by the Institute for Economics and Peace (IEP), a global think tank headquartered in Sydney, Australia.In 2017, Prieto-Curiel and Bishop developed a mathematical model to predict the factors that shape people’s perception of safety. Their findings revealed that fear of crime is contagious and that it often takes only a couple of incidents in a place for people to feel worried, even if they live in relatively safe areas. The model also showed that a drop in actual crime does little to change people’s perception of security.Breaking the cartel black boxOver the past decade, the Mexican government has tried various strategies to tackle cartels and organized crime, from targeting drug lords to increasing investment in social programmes to prevent people from joining gangs. Overall, it spends almost $10 billion each year on security and roughly $9 billion on social programmes, according to government figures. But these approaches have done little to weaken the cartels’ grip on the country, with organized crime continuing to be a principal driver of extreme violence, the IEP report notes.Demonstrators took to the streets of Mexico City to protest against cartel violence in November 2025.Credit: Marian Carrasquero/Bloomberg via GettyIn February 2022, 17 people were shot dead outside a funeral wake in the town of San José de Gracia in Michoacán, a state that has long been wracked by violent turf wars between cartels. Prieto-Curiel heard López Obrador describe the event in the media as the ‘settling of scores’ among cartels. In other words, López Obrador was arguing that Mexico’s violence was driven mainly by cartel members killing each other rather than civilians. But if this were true, their size should have shrunk over the years, not increased as several statistics have shown, says Prieto-Curiel. This suggested something else was going on. “That was the moment I realized the way we look at cartels is wrong,” he says.Because of their secrecy, studying cartels is notoriously difficult — a black box, says Prieto-Curiel. To try to overcome this, he and his colleagues used public data on homicides, prison incarcerations and missing persons over the past decade to build a mathematical model of cartels’ activities. The researchers simulated different policy scenarios, such as increased incapacitation (when cartel members are incarcerated or arrested) and greater efforts to prevent people from joining organized crime groups, to predict the effects of various strategies on violence and cartel size.Prieto-Curiel’s model showed that cartel members had risen from 115,000 in 2012 to 175,000 in 2022, which was roughly the entire prison population of Mexico that year, he says. The 2022 figure makes cartels the fifth-largest employer in the country, beating the national convenience-store chain Oxxo, which employs around 168,000 people. Around one-third of all active cartel members are part of the three most powerful organizations: the Jalisco Nueva Generation (CJNG), Sinaloa (CDS) and Nueva Familia Michoacana cartels, according to the model.The model showed that, in 2021 alone, the cartels recruited 19,300 people and lost 12,200 members to conflicts and incarcerations. That means cartels must recruit between 350 and 370 people each week to prevent their organizations from collapsing, says Prieto-Curiel.When the researchers forecast different future scenarios, the picture was grim. If the government made no changes to current strategies to tackle cartels, there would be 40% more casualties by 2027, with the cartels growing by 26%. Meanwhile, doubling incarcerations would still lead to an increase in violence. “That result is one of the darkest results I have ever had in my research career,” he says.Rafael Prieto-Curiel presents his work at the Falling Walls Science Summit in Berlin.Credit: Anja BöckBut Prieto-Curiel’s modelling also revealed what could curb cartel violence. If there were a way to block cartels from recruiting members, this would cut casualties by one-quarter and reduce cartel size by 11% by 2027. This suggests that policies that aim to prevent people from joining organized crime groups could be more effective at reducing violence than are policies that focus solely on incarceration, says Prieto-Curiel.