University of New Hampshire Scholar Rachel Trubowitz Speaks on Origin of ‘Paradigm-Shifting’ Acceptance of Infinity in Mahindra Center Talk

Rachel Trubowitz, an English professor at the University of New Hampshire, spoke about how the widespread acceptance of infinity allowed for the development of modern science and mathematical concepts, despite being initially feared, at a Thursday talk.

Trubowitz has spent much of her career researching 17th century literature and culture, including the works of English author John Milton — famous for his poem “Paradise Lost,” which describes the biblical fall of man. She centered much of her lecture on her new book, titled “Milton in Mathematics,” which is currently under review at Cambridge University Press.

Trubowitz built her argument on three key areas: the development of new mathematical tools, the slow acceptance of infinity as a legitimate concept, and the ensuing philosophical paradigm shift. Speaking at the Women, Gender, and Culture in the Early Modern World seminar hosted at the Mahindra Humanities Center, Trubowitz linked the positive acceptance of infinity among scientists and mathematicians to broader rejection of classical theological and hierarchical thought.

Trubowitz centered her remarks on arguments from her monograph — entitled “Milton in Mathematics,” which is currently under review at Cambridge University Press — and argued that Cavendish and Milton took the mathematics of infinity and turned it into a model of nature and politics.

According to Trubowitz, political thought surrounding hierarchical social structures changed because people’s perception of God shifted as the idea of infinity became more accepted.

Trubowitz began by explaining that Ancient Greek myth and philosophy formed the foundation for scientific thought for centuries, where the potential existence of an infinity implied the existence of nothing and was treated as a horrific concept.

She also pointed to the way that the acceptance of infinity shaped the foundations of modern math, including calculus and physics. She referenced influential scientists like Isaac Newton and Gottfried Wilhelm Leibniz, whose work uncovered mathematical tools that depended on the existence of infinity.

Extending her analysis beyond the mathematical world, Trubowitz explored how some of Cavendish and Milton’s key ideas tied to theological concepts of God’s omnipotence. She noted that these beliefs extended further to political thought, shaping theories of governance.

“In short, Cavendish and Milton allow us to see that the new paradigm concerning interoperating relations between the infinite and the finite can serve both conservative and liberal politics, and both traditional and radical theology,” she said.

This new understanding that infinity not only existed, but was useful, was soon applied to philosophical thought, Trubowitz argued.

“Early modernity’s mathematical innovations concerning infinity and the conflicts they inspired were appropriated by religious and political institutions to create a proxy war over whether modern Europe would be rigidly hierarchical or open and quasi-democratic,” Trubowitz explained.

Some attendees of Thursday’s talk challenged parts of Trubowitz’s interpretation of the “radical, pivotal, and paradigm-shifting” acceptance of infinity as a concept, and asked for clarity on her explanation of how scientists like Newton fostered social acceptance of infinity.

Trubowitz invited her colleague Nathan Schwadron, an astrophysics professor at the University of New Hampshire, to elaborate on the scientific consensus over Zoom during the talk. Schwadron said Newton’s results came as a surprise, going against the grain of accepted science at the time.

“Newton, who was very, very interested in proving stability — proving this very, very deterministic nature of physics — actually led directly to show that in normal in-body problems, such solutions can have absolutely no solution at all,” Schwadron said. “Newton, by trying to prove the finite, ended up proving the infinite.”

Trubowitz ended her remarks by calling for more interdisciplinary research, noting that scientists and humanities scholars were once the same, and still have much to learn from each other today.

“I think there’s a place for a merger of science and humanities,” Trubowitz argued. “I think there must be some way that the humanities can teach something to scientists, and I think all humans should be scientifically literate.”