b. 1943
Geoffrey Hellman is an American philosopher of mathematics at the University of Minnesota, best known for developing modal structuralism as an alternative to platonism. His 1989 book Mathematics Without Numbers argues that mathematical claims are best understood as modal assertions about possible structures rather than claims about abstract objects. He has also contributed to the philosophy of quantum mechanics and the foundations of mathematics more broadly.
Developed modal structuralism in Mathematics Without Numbers (1989)
Provided a nominalist-friendly reconstruction of classical mathematics using modal logic
Critiqued Jerrold Katz's platonist argument by elimination
Contributed to the foundations of real analysis and the philosophy of mathematical practice
Co-authored work on structuralism and the ontology of mathematics with Stewart Shapiro