Harvard Mathematics professor Lauren K. Williams has been named a 2025 MacArthur Fellow, the foundation announced on Wednesday, as reported by the Harvard Crimson. The award, known as the MacArthur “Genius Grant,” provides $800,000 over five years with no restrictions. It recognizes exceptional creativity and potential for future contributions in a wide range of fields.
Williams was recognized for research that bridges theoretical mathematics and physics. She studies algebraic combinatorics , a field that uses algebra to understand discrete structures. Her work on the positive Grassmannian, a geometric space that encodes all planes of a given dimension, has advanced understanding in both mathematics and physics. She also studies the amplituhedron, a structure that helps physicists model particle interactions, as well as Macdonald polynomials and cluster algebras, which explore connections between algebraic and geometric structures.
Fellowship provides financial securityThe award comes at a challenging moment for Williams and other researchers at Harvard. Earlier this year, the Trump administration froze $2.2 billion in National Science Foundation grants, temporarily cutting funding for hundreds of projects. A federal judge later ordered the funds restored, but many researchers, including Williams, are still waiting for the money. The MacArthur Fellowship provides unrestricted support, allowing her to continue research without dependence on federal funding.
Academic journeyWilliams’ interest in mathematics began in elementary school, after early success in a local math contest, according to The Harvard Crimson. She studied mathematics at Harvard, graduating in 2000, and then earned a Ph.D. from the Massachusetts Institute of Technology in 2005. Her dissertation focused on combinatorial aspects of total positivity.
After several years teaching at the University of California, Berkeley , she returned to Harvard in 2018. She became the second woman to earn tenure in the Mathematics Department’s history. Her career has combined research, teaching, and mentoring, shaping the next generation of mathematicians.
Research and impactWilliams’ work is highly theoretical but has applications across multiple disciplines. Her studies in algebraic combinatorics connect mathematics to physics, representation theory, and geometry. By exploring geometric structures such as the positive Grassmannian and amplituhedron, her research provides new ways to model and visualize complex systems.
The MacArthur Foundation highlighted Williams’ ability to elucidate unexpected connections in mathematics. Her interdisciplinary approach demonstrates the growing links between abstract mathematics and practical problems in physics and other scientific fields.
Contribution to educationWilliams has emphasized that advanced mathematical concepts can be introduced in accessible ways. She has developed methods to teach abstract ideas at a fundamental level, making them understandable for students. Her career serves as a model for aspiring mathematicians, particularly women, in a field where female representation remains low.
Her MacArthur Fellowship allows her to continue both her research and her work mentoring students. It also highlights the importance of supporting fundamental research, even in times of funding uncertainty, and underscores the impact of curiosity-driven inquiry on scientific progress.
Williams was recognized for research that bridges theoretical mathematics and physics. She studies algebraic combinatorics , a field that uses algebra to understand discrete structures. Her work on the positive Grassmannian, a geometric space that encodes all planes of a given dimension, has advanced understanding in both mathematics and physics. She also studies the amplituhedron, a structure that helps physicists model particle interactions, as well as Macdonald polynomials and cluster algebras, which explore connections between algebraic and geometric structures.
Fellowship provides financial securityThe award comes at a challenging moment for Williams and other researchers at Harvard. Earlier this year, the Trump administration froze $2.2 billion in National Science Foundation grants, temporarily cutting funding for hundreds of projects. A federal judge later ordered the funds restored, but many researchers, including Williams, are still waiting for the money. The MacArthur Fellowship provides unrestricted support, allowing her to continue research without dependence on federal funding.
Academic journeyWilliams’ interest in mathematics began in elementary school, after early success in a local math contest, according to The Harvard Crimson. She studied mathematics at Harvard, graduating in 2000, and then earned a Ph.D. from the Massachusetts Institute of Technology in 2005. Her dissertation focused on combinatorial aspects of total positivity.
After several years teaching at the University of California, Berkeley , she returned to Harvard in 2018. She became the second woman to earn tenure in the Mathematics Department’s history. Her career has combined research, teaching, and mentoring, shaping the next generation of mathematicians.
Research and impactWilliams’ work is highly theoretical but has applications across multiple disciplines. Her studies in algebraic combinatorics connect mathematics to physics, representation theory, and geometry. By exploring geometric structures such as the positive Grassmannian and amplituhedron, her research provides new ways to model and visualize complex systems.
The MacArthur Foundation highlighted Williams’ ability to elucidate unexpected connections in mathematics. Her interdisciplinary approach demonstrates the growing links between abstract mathematics and practical problems in physics and other scientific fields.
Contribution to educationWilliams has emphasized that advanced mathematical concepts can be introduced in accessible ways. She has developed methods to teach abstract ideas at a fundamental level, making them understandable for students. Her career serves as a model for aspiring mathematicians, particularly women, in a field where female representation remains low.
Her MacArthur Fellowship allows her to continue both her research and her work mentoring students. It also highlights the importance of supporting fundamental research, even in times of funding uncertainty, and underscores the impact of curiosity-driven inquiry on scientific progress.
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