One can argue that no science is capable of finding all counterexamples to a theory, therefore, no science is strictly empirical, it's all quasiempirical. But usually, the term 'quasiempirical[?]' refers to the means of choosing problems to focus on (or ignore), selecting prior work on which to build an argument or proof, notations for informal claims, peer review and acceptance, and incentives to discover, ignore, or correct errors. These are common to both science and mathematics  and do not include experimental method.
Post20thcentury philosophy of mathematics is mostly concerned with quasiempirical methods especially as reflected in actual mathematical practice of working mathematicians.
See also: quasiempiricism in mathematics, empirical methods, philosophy of science, philosophy of mathematics, mathematical practice.
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