How an Uzbek mathematician became an AI Safety researcher at Stanford

Abdumalik Abdukayumov, City — Palo Alto, PhD Student at Stanford University, Instagram

About Me

I am from Uzbekistan. I studied at the International Mathematics School in Karakul and then studied economics and finance at Tashkent State University of Economics. In Tashkent, I devoted most of my time to scientific research in the field of probability theory. Three years ago, I moved to the United States and earned a master’s degree in economics and IT at Duke University. Currently, I am a first-year PhD student at Stanford University. My research interests include optimization, machine learning, as well as AI Alignment and AI Safety.

How I Entered the Field of AI Research

At Duke University, I had the opportunity to engage in research in machine learning and statistics. I realized that I could leverage my background to improve the efficiency of AI models and solve complex problems. Since my research interests are focused on optimization, I naturally gravitated toward this topic and the field of AI Research, where algorithmic efficiency plays a key role.

My research career began with a strong mathematical foundation. When I participated in International Mathematics Olympiads, our main sponsors were companies like Jane Street and other leading financial firms. They often hire olympiad winners. Unfortunately, in Uzbekistan, we did not have the opportunity to work there directly. Therefore, my friend and I founded our own hedge fund, where I took on the position of lead quantitative researcher. Thanks to my previous research experience in probability theory, I successfully handled this role. We developed algorithms and solved complex optimization problems. Unfortunately, we closed the fund in 2022, and shortly before starting my master’s program at Duke, I managed to complete an internship at the Central Bank of Uzbekistan in the Department of Financial Stability. It was this applied and pure research experience that pushed me to delve deeper into scientific research.

I chose Stanford GSB because it is a unique place that combines rigorous academic research with close proximity to Silicon Valley. My program—a PhD in Operations, Information and Technology—is ideally suited to my goals. First, OIT allows for deep theoretical research in optimization and stochastic models, which form the foundation for reinforcement learning and AI safety. Second, Stanford encourages an interdisciplinary approach, giving me the opportunity to collaborate with experts from the Computer Science department and the Stanford HAI center. Additionally, proximity to industry leaders allows me not only to develop theory but also to work on applied AI Alignment tasks in real time. It is important to me that my research has practical applications and helps make artificial intelligence systems more robust and safe.

How the PhD Application Process Went

The selection process at Stanford is extremely competitive. This year, only three people were admitted to my OIT group for the PhD program. For admission to such a program, it is critically important to have a strong mathematical foundation. In my case, I believe that my medals from International Mathematics Olympiads, which I won in school and university, were a huge advantage. This served as proof that I possess the necessary analytical thinking to conduct complex research. Furthermore, for world-class PhD programs, research experience is decisive. Before admission, I closely collaborated with Professor Yehua Wei at the Fuqua School of Business. My work focused on optimization and learning algorithms, specifically extending multivariate prophet inequalities. This experience allowed me to show the admissions committee that I was already ready for independent scientific activity. Given that the acceptance rate at Stanford GSB is less than 5%, the combination of my olympiad background and real academic publications became my key to success.

My training in economics and algorithmic game theory is one of my main advantages in AI research, especially in areas such as AI Alignment and AI Safety. First, the problem of AI Alignment is essentially a mechanism design task. We try to design incentives and reward functions so that the behavior of an AI agent aligns with human values. Game theory provides a rigorous mathematical framework for modeling these interactions. Second, modern AI methods, especially reinforcement learning, are built on the same fundamental principles as mathematical economics: optimization and stochastic processes. My experience with prophet inequalities and regret bounds is directly applicable to analyzing the efficiency and reliability of learning algorithms. Finally, when we consider systems with multiple autonomous agents, game theory becomes the only way to predict and stabilize their behavior to avoid unpredictable or dangerous consequences. My interdisciplinary background allows me to look at AI safety problems not just as an engineering task, but as a complex system of incentives and strategic decisions.

Challenges

Transitioning from theoretical mathematics and economics to technical AI was an interesting challenge. I would highlight two main difficulties. First, the shift from “proof-based” thinking to “experimental” thinking. In mathematics, we are used to working within strict proofs: if a theorem is proven, it is always true. In deep learning and RL, theory often follows practice. I had to learn to work in conditions where I needed to conduct numerous experiments, tune hyperparameters, and analyze empirical results that do not always lend themselves to immediate theoretical explanation. Second, the engineering aspect. Although I had a programming base, modern AI requires deep mastery of a specific stack: PyTorch, GPU computing, and efficient implementation of complex optimization algorithms. However, my experience in mathematics olympiads helped me greatly. The olympiad background trained me to quickly understand new abstract structures and find non-standard solutions. Thanks to this, I was able to quickly master the necessary tools and focus on the main thing—how my knowledge in optimization can improve the safety and reliability of AI systems.

Dead ends are inevitable in scientific work—they are part of the process of discovering new knowledge. When I hit a research dead end, I use several proven approaches:

1. My olympiad experience taught me that if a problem cannot be solved for a long time, perhaps I made a false assumption at the very beginning. I try to simplify the model to a basic level and check if my ideas work on the most elementary example.
2. One of the main advantages of studying at Stanford is access to outstanding experts. I often discuss my difficulties with colleagues or my scientific supervisor. Sometimes an outside perspective helps to see what I missed due to deep immersion in details.
3. If I feel that I am “stuck,” I temporarily switch to another task—for example, programming or reading literature on a related topic. Often, the solution comes precisely during such an intellectual pause.
4. I write down why a particular path did not work. In research, a negative result is also a result. This helps me systematize the process and avoid repeating the same mistakes in the future.

This approach allows me to maintain motivation and turn every difficulty into a step toward the correct solution.

One of the most serious technical tasks I worked on was research at Duke University in collaboration with Professor Yehua Wei. We worked on extending multivariate prophet inequalities for complex decision-making scenarios. The main technical difficulty lay in the “curse of dimensionality.” In multidimensional settings, the number of constraints in an optimization problem usually grows exponentially, making standard computational methods practically useless. My task was to find a way to make this model computationally efficient without losing accuracy. To solve this problem, I developed a linear programming formulation with a polynomial number of constraints instead of an exponential one. This required a deep application of stochastic modeling and combinatorial optimization tools. As a result, we managed to prove new regret bounds for learning algorithms. This experience was extremely important for my current work in AI Safety: it taught me that the safety and reliability of AI systems begin with mathematically provable guarantees of algorithm behavior, especially under conditions of high uncertainty.

Recommendations

Based on my experience transitioning from pure mathematics to AI safety research, I would give three main pieces of advice:

1. Strengthen your mathematical foundation. AI Safety is not just philosophy; it is a strict technical discipline. A deep understanding of probability theory, optimization, and stochastic processes is the foundation that will allow you not only to use existing models but also to create new methods for verifying their safety. My olympiad background has saved me many times when solving problems where standard methods did not work.
2. Study game theory and incentive economics. The Alignment problem is largely about how to make a system pursue the goals we have instilled in it, avoiding “reward hacking.” Knowledge of game theory will help you better understand how to design reward functions and analyze agent behavior in complex environments.
3. Do not be afraid of interdisciplinarity and early participation in research. AI Safety requires ideas from a wide variety of fields—from computer science to political economy. Look for opportunities to work on real projects with professors or in research laboratories. The practice of working on a real article or algorithm teaches much more than just reading literature.

Remember that this field is still young, and right now you have the chance to contribute to what the future of humanity will look like in the era of superintelligence.