Quasi-empiricism in mathematics is a philosophical approach that redirects attention from abstract foundational issues to the actual practice of mathematics, particularly its close relationships with physics, social sciences, and computational fields. In 1960, Eugene Wigner famously noted the "unreasonable effectiveness" of mathematics in physics, suggesting this might stem from human cognitive biases and a "wonderful gift" we neither understand nor deserve. Richard Hamming, in 1980, argued that successful applications sometimes trump formal proof, positing that real-world utility can solidify mathematical theorems even if their proofs face issues.
Willard Van Orman Quine (1960) connected this by suggesting the same evidence supports theorizing about both the world's structure and mathematical structures. Later, Hilary Putnam (1975, 1983) observed that mathematics has historically accepted informal proofs, made and corrected errors, and developed differently across cultures, leading many to advocate for a "quasi"-empirical method—embracing a scientific approach for consensus within an international mathematical community. This perspective emphasizes the practical, evolving, and interconnected nature of mathematics rather than solely its logical purity.