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An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right. Coq is an interactive theorem prover first released in 1989. It allows for expressing mathematical assertions, mechanically checks proofs of these assertions, helps find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
The quality of implemented systems has benefited from the existence of a large library of standard benchmark examples—the Thousands of Problems for Theorem Provers (TPTP) Problem Library [25] —as well as from the CADE ATP System Competition (CASC), a yearly competition of first-order systems for many important classes of first-order problems.
Starting in 2004, [7] Salman "Sal" Khan began tutoring one of his cousins in mathematics on the Internet using a service called Yahoo! Doodle Images. [8] After a while, Khan's other cousins began to use his tutoring service. Due to the demand, Khan decided to make his videos watchable on the Internet, so he published his content on YouTube. [9]
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SageMath is designed partially as a free alternative to the general-purpose mathematics products Maple and MATLAB. It can be downloaded or used through a web site. SageMath comprises a variety of other free packages, with a common interface and language. SageMath is developed in Python.
The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution.
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