Define tangible benefits and give example of any pure mathematics in last 200 years having tangible benefits.

One benefit is that it is related to foundations of mathematics. If you can find busy beaver number 745, you can prove or disprove Maths. If you can find busy beaver 6, you can prove few collatz like conjecture which is an open problem.

Most core research doesn't help directly, but through indirect means. e.g. This would have led to finding the areas of improvements in Lean due to its complexity. I know for fact that Lean community learns a lot from projects like Mathlib and this. And Lean is used in all sort of scenarios like making AWS better to improving safety of flights.