What is Lambda Calculus

What is it ? and Why is it useful ?

Leibniz had as ideal the following. Create a ‘universal language’ in which all possible problems can be stated. Find a decision method to solve all the problems stated in the universal language. If one restricts oneself to mathematical problems, point of Leibniz’ ideal is fulfilled by taking some form of set theory formulated in the language of first order predicate logic. This was the situation after Frege and Russell (or Zermelo). Point of Leibniz’ ideal became an important philosophical question. ‘Can one solve all problems formulated in the universal language?’ It seems not, but it is not clear how to prove that. This question became known as the Entscheidungsproblem.

The basis of almost all functional programming, Professor Graham Hutton explains Lambda Calculus in this great video