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Matthew Harrison-Trainor, a mathematician at the University of Illinois Chicago, has been awarded the Sloan Research Fellowship, one of the most prestigious awards for early-career researchers.

Harrison-Trainor, an assistant professor in the Department of Mathematics, Statistics and Computer Science, was one of 126 researchers chosen for the 2024 class of Sloan Research Fellows announced Tuesday, Feb. 20. He is the 21st UIC faculty member and the 16th from mathematics to receive the honor.

The fellowship gives Harrison-Trainor a two-year, $75,000 award to advance his research. It also inducts him into a select group that includes 57 Nobel Prize recipients and 17 winners of the Fields Medal in mathematics.

Harrison-Trainors work sits at the intersection of mathematics and computer science. It draws on mathematical logic and computability theory, a field that early computing pioneer Alan Turing originated.

A lot of computer science is about how efficiently things can be done. What I do is ask, Can you do it at all?, Harrison-Trainor said. We can imagine that in the future we will make better computers. But there are still problems that, no matter how good our computers are, were still not going to be able to do. Computability theory is about finding those boundaries.

In theoretical computer science, mathematicians study the complexity of computational problems, determining if they would be solvable in a reasonable length of time. Harrison-Trainors work goes a step further to determine if those problems are solvable at all.

In mathematics, researchers try to break complex phenomena into simple components to explain how they work, such as proving whether two complex geometric spaces are identical based on only a small set of observations. But sometimes they hit boundaries where the components cant be simplified any further. Harrison-Trainors work can help people pursuing these problems determine if theyve arrived at the limit of explainability.

Its like trying to explain the functions of the human brain by observing the activity of every individual neuron, Harrison-Trainor said. Such a model would not only be computationally intensive or impossible it would fail to improve our understanding of how the brain works. That isnt an explanation; it doesnt simplify whats going on, Harrison-Trainor said.

For certain mathematical problems, you can actually prove that theres no simple understanding, Harrison-Trainor said. Its not just that we havent come up with one yet, you can show that were never going to be able to.

Harrison-Trainor credited the UIC mathematics community and its historical strength in mathematical logic with supporting his Sloan fellowship application. Hes also a part of the mathematical computer science group, which brings together faculty and students working on problems at the intersection of mathematics and computer science.

Theres a strong community in the study of logic in the Midwest, and UIC is part of that, Harrison-Trainor said. Its a strong department, and when you have strong people, more good people and students come in.

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Mathematician Matthew Harrison-Trainor receives Sloan Research Fellowship | UIC today - UIC Today