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Portrait of Matthew Foreman leaning against a tree trunk in a forest background

‘Impossibility Results in Mathematics’: Lonseth Lecture 2025

By Arie Henry

“You can't square the circle!”

“The square root of 2 can't be written as a fraction!”

“The integral of e^{-x^2} can't be written in closed form!”

“Bitcoin is unbreakable!”

Most of mathematics is about finding solutions to problems or approximating them well. But there is an important collection of results that show certain tasks are mathematically impossible. At this year’s Lonseth Lecture, mathematician Matthew Foreman explains what that means, and the varying notions of impossibility:

40th Annual Lonseth Lecture

Date: Thursday, May 1, 2025
Time: Department awards at 3:30 p.m.; lecture at 4 p.m.; reception to follow
Location: LaSells Stewart Center, Construction and Engineering Hall

We'll begin by honoring student and faculty achievements at our annual awards ceremony from 3:30 to 4 p.m. Then we'll settle in for the lecture, given by Matthew Foreman, from 4 to 5 p.m. A public reception will follow immediately after.

About the speaker: Foreman's mathematics career began very young, receiving his bachelor's degree at the age of 18. He earned his Ph.D. in 1980 at University of California, Berkeley under the direction of Robert M. Solovay. In 1994, he answered a 60-year-old problem about the Banach-Tarski paradox by showing that there is a paradoxical decomposition of the sphere using pieces with the property of Baire. Today, he is a set theorist at University of California, Irvine and has made contributions in widely varying areas of set theory, including descriptive set theory, forcing and infinitary combinatorics.


Established in 1985, the Lonseth Lecture series pays tribute to the legacy of Arvid T. Lonseth, a respected figure in the Mathematics Department at Oregon State University. Explore more about Arvid Lonseth and the lecture series to appreciate its significance within academia.


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