Z is an interactive theorem prover designed to be both easy to learn, yet powerful enough to allow complex mathematical proofs. It was created by the Oxford University Computing Laboratory and is now used by many universities and research laboratories around the world.

Z is a powerful logic-based system used to describe and represent Mathematical assertions made by proving the validity of steps. It uses a formal language called Z-notation which stands out for its use of characters and indentation to create a readable, structured ‘text’. Z-notation is easy to learn and provides an unambiguous way of expressing mathematical statements, proof steps, and axioms (laws of mathematics).

Since its introduction in the late 1970s, Z has become the de facto language for formal proof development in the world of academia. This is due it its expressive power and its ability to represent mathematical concepts. It also enables powerful tools to help automate processes such as verifying and validating mathematical proofs. This saves time and greatly reduces the chance of error.

The software is extremely versatile and can be used for a wide range of applications. Z can be used for developing models of a system, such as a computer network, or for developing complex algorithms. It is an incredibly valuable intellectual tool because it turns traditionally informal and often tedious problem-solving processes into a rigorous and structured set of steps. It also enables the creation of robust models to represent realistic scenarios.

Z is now used in many different scientific fields, such as economics, computer science, philosophy, and physics, as well as areas of mathematics such as algebra, geometry, logic, calculus and set theory.

The beauty of Z is its power and flexibility: it is powerful enough to prove complex theorems, yet simple enough to use for everyday applications. The Z system has a general purpose, making it applicable to verifications of all kinds, ranging from engineering and financial systems to medical and bio-informatics systems. It is designed to not only enable proof by computation but to enable its users to understand why their proofs are correct.

Overall, Z stands out as a powerful tool to help theoretical and applied mathematicians develop and verify their mathematics. Its widespread use and increasing popularity indicates that it is here to stay, and will continue to help scientists discover new facts and gain insight into the world of mathematics.