Unlocking the Math Behind Better Decisions

Beneath your fingertips, a single tap on a phone screen initiates a chain reaction of algorithmically-powered interactions designed to instantaneously convert requests into reality. Hidden in plain sight, mathematics is inextricably woven through the operations of daily life—like when ridesharing apps match riders to drivers, set prices, or decide when price surges occur.

Operations research is the field crafting these invisible interactions, helping organizations and platforms model business patterns and operations using algorithms and mathematical models. Companies hire applied mathematicians to design these systems and keep improving them—work that occasionally runs into hard, precisely stated mathematical problems.

And like every other sector, the field of operations research is being totally upheaved by the rapid progression of AI.

For pure and applied mathematicians, AI is being put to work cleaning up the debris—unsolved math problems that have piled up in the field’s journals—from years of research. Freed from the challenge and tedium of these lingering questions, math experts are now facing a new, more expansive meta-math realm ready to be explored. And this new realm of “mathematics in the age of AI” is now reaching into theoretical operations research as well.

Researchers at Chicago Booth have designed an AI system that unearths unsolved math problems in the field—first extracting them from the leading academic journals of operations research and operations management (OR/OM) and of the neighboring field at the intersection of economics and computer science (Econ/CS), and then putting AI’s math skills to the test, at scale, through an automated pipeline.

The experimental study has a dual goal: to showcase what off-the-shelf AI tools can do in theoretical operations research, and to help the research community weave such pipelines into its own workflows. It was led by Rad Niazadeh, Associate Professor of Operations Management at the University of Chicago Booth School of Business, and Pranav Nuti, Principal Researcher at Chicago Booth, with support from Eric Fithian, Predoctoral Researcher at the Center for Applied AI.

Meta Math: New Paradigms and Possibilities

With new, seemingly magical AI tools, some researchers are turning to LLMs to solve questions that have stumped mathematicians for decades—like those of mathematician Paul Erdős, left unsolved since the 1940s. Several teams, including large groups at OpenAI and Google DeepMind—are similarly investigating abstract problems of pure mathematics.

Niazadeh and Nuti set their sights on a different target: the everyday unsolved—open—problems of their own field. What if AI could sift through an entire academic journal to find the questions that papers pose and leave unresolved and then go to work solving them, one after another?

Three research questions drive the project: How effective are existing frontier LLMs at solving these open problems? Can an agentic pipeline solve them at scale? How can access to these tools be democratized to enable more researchers to join the effort? 

The team got to work testing their agenda on unsolved problems in OR/OM and Econ/CS. As the agents work through problem after problem, mathematicians working on operations obstacles are now empowered with a repository of open problems, literature reviews, and solution attempts from across the enormous field of operations research.

Even researchers working at the forefront of discovery and knowledge creation face friction. In the most popular academic journals, hundreds of problems are left unsolved. These “open problems” are lingering mathematical queries that create friction and uncertainty. For Niazadeh and Nuti, this was new territory ripe for automated exploration.

The field’s problems also have a particular character. Questions in OR/OM and Econ/CS stem from real-world problems like how to fairly allocate resources, or how to design marketplaces that respond to strategic behavior. They deal with more concrete structures and tangible outcomes with observable impacts on human life—unlike the abstraction characteristic of pure mathematics.

Operations problem-solving tends to follow a recognizable playbook: first, spot patterns and connections between problems, apply tools from one subsect of OR to other similar areas, identify decode easier special cases, and hunt for counterexamples that guide the design of an algorithm or mechanism.

Companies who hire mathematicians to think through operations problems have been somewhat limited by the specific area of expertise in which an employee is trained—a specialist in rational behavior or game theory comes with a different set of specialty tools and foundations than one trained in stochastic systems. AI tools help immensely in removing this obstacle.

Case in point: Niazadeh and Nuti’s AI tools have read publications from across all corners of the operations research spectrum, and the result is a public, browsable database of the field’s unsolved questions. Each question is cleanly rewritten and paired with a literature review along with every recorded solution attempt.

Much like an architect studying biology to learn about structurally sound design tested and strengthened by years of evolution, AI-empowered mathematicians can tap into other ways of going about their work. “I learn new techniques for problem-solving that come from different areas in the field of math,” said Nuti. “These tools have exposed me to findings and ideas and create new pathways for study that I wouldn’t otherwise encounter.” Empowered with new ideas, new solutions are being unlocked at exponential rates.

An Ecosystem of Agents

Trained to read through publications, the research team customized an off-the-shelf LLM capable of sifting through open problems which were then given to an AI agent prompted to automatically find solutions. The team designed an entire agentic pipeline, whereby agents would formalize, verify, and reformat operations research problems from a leading academic journal, Mathematics of Operations Research, covering every paper the journal published over the last three years. After conducting due diligence reviews of literature, a team of customized agents—solvers, verifiers, formatters, judges—systematically coordinated to find the best possible solutions.

“We’ve created an ecosystem of LLM-based agents that work on the problem together, and talk to one another,” Nuti explained. “One agent is in charge of extracting the problem from the paper, another is in charge of verifying whether that problem is solved in the literature by searching the web.” From there, solver agents take the attempt to solve the problem and find gaps, send objections, and repeat the cycle. After multiple iterations through the ecosystem, agents circle around and home in on accurate solutions.

By the end of their initial trial, the collective of agents successfully extracted 132 problems, and solved 26—with partial progress on more than one hundred more—without any human intervention. As a fail-safe, the team personally reviews the solutions from the multi-agent team of AI ‘mathematicians.’ The first AI-generated solution to be fully vetted, an answer to a question about fair resource division, passed team standards with flying colors.

A modest-sounding success rate, the 26 solved problems indicate AI’s strength in a particular kind of task: hunting down counterexamples to disprove a hunch. “Current LLMs excel in finding certain examples that might show that some thought you had is not actually true,” said Nuti. Humans, by contrast, tend to fixate on an idea they are trying to prove and unintentionally look for evidence in their favor—a bias models simply do not have. AI agents are also empowered with a near-infinite capacity to remember information from enormous pools of data—another skill outside of the scope of the average human brain.

Abstract Thinking

In a universe where question-asking potential is infinite, but computing power is not, having AI lighten the load of solving tedious, lingering problems means mathematicians can zoom out to more meta ideas. The human brain simply lacks the ability to remember the location of every single unsolved problem in hundreds of academic papers and find patterns or recurring thoughts.

That comes with a caution. “To become a better mathematician, you need to think through the problem yourself, to create those pathways in your head,” Nuti said. He follows a personal rule of keeping one day each week free of any AI tool, instead working problems by hand and mind. Foundational mind patterning lays the groundwork for the more abstract, complex thinking characteristic of what is now possible with AI. Used well, AI models free researchers to play with more ideas than time would allow, running dozens of different approaches in parallel.

Problem-solving Democratized

As abstract or meta as the math behind operations research may feel, the study demonstrates just how feasible it is to use the most common AI models for even highly nuanced tasks. Building pipelines—or communities—of agent processes and interactions is accessible to any user of the most widespread, public models like ChatGPT or Claude. “Ready-to-use, large AI models empower us to carry out numerous iterations of multi-agent problem solving until they find a solution, all in an automated fashion,” said Niazadeh.

The project sets forth a new paradigm of problem-solving in research: teams of specialist agents leverage their expert skillsets to develop a coordinated approach. By tapping publications from across the spectrum of operations research, the study demonstrates the value of looking beyond the narrow silos of academic research and turning to other disciplines for inspiration. Solving problems, in this way, is predicated upon community collaboration.

To extend this collaborative approach, all prompts used to develop the agents used in this project as are publicly available. The results of every solution attempt, successful or not, as well as problem statements and literature reviews can be reviewed on the project website, which is regularly updated with novel solutions.

Keeping every attempt, including the failures, is intentional: when researchers experiment with AI on their own, unsuccessful tries simply vanish, and the next person starts from scratch. Recorded in a shared database, those attempts become collective memory for the next researcher—human or AI—to expand upon and refine.

This research was supported by the Center for Applied Artificial Intelligence throughout the 2025-2026 Academic Year.