it's part of theoretical computer science. You asking this is the same as someone in the 15th century asking why bother with square root of negative 1, and what

it's part of theoretical computer science. You asking this is the same as someone in the 15th century asking why bother with square root of negative 1, and what it could possibly be used for. lambda calculus can be considered fundamental to how computations can be represented via simple building blocks - it's in the same category as a turing machine. if a problem could be represented as a lambda calculus expression, you know that it is theoretically solvable - or if you proved that it isn't, then you know the problem is unsolvable (like the halting problem).