Albert Einstein's discovery of the general relativity theory relied upon thought experiments and mathematics. Empirical methods only became relevant when confirmation was sought. Furthermore, some empirical confirmation was found only some time after the general acceptance of the theory.
Thought experiments are almost standard procedure in philosophy, where a conjecture is tested out in the imagination for possible effects on experience; when these are thought to be implausible, unlikely to occur, or not actually occurring, then the conjecture may be either rejected or amended. Logical positivism was a perhaps extreme version of this practice, though this claim is open to debate.
Quasi-empiricism in mathematics is an important topic in post-20th-century philosophy of mathematics, especially as reflected in the actual mathematical practice of working mathematicians.
Lolli, Gabriele (2008). "Experimental Methods in Proofs". Deduction, Computation, Experiment. pp. 65–79. doi:10.1007/978-88-470-0784-0_4. ISBN 978-88-470-0783-3. 978-88-470-0783-3 ↩