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2. Lean (proof assistant) - Wikipedia

   en.wikipedia.org/wiki/Lean_(proof_assistant)

   Lean is a proof assistant and a functional programming language. [ 1] It is based on the calculus of constructions with inductive types. It is an open-source project hosted on GitHub. It was developed primarily by Leonardo de Moura while employed by Microsoft Research and now Amazon Web Services, and has had significant contributions from other ...

3. Millennium Prize Problems - Wikipedia

   en.wikipedia.org/wiki/Millennium_Prize_Problems

   e. The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$ 1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...

4. Generative pre-trained transformer - Wikipedia

   en.wikipedia.org/wiki/Generative_pre-trained...

   Generative pretraining (GP) was a long-established concept in machine learning applications. [16] [17] [18] It was originally used as a form of semi-supervised learning, as the model is trained first on an unlabelled dataset (pretraining step) by learning to generate datapoints in the dataset, and then it is trained to classify a labelled dataset.

5. OpenAI unveils newest AI model, GPT-4o - AOL

   www.aol.com/openai-unveils-newest-ai-model...

   The new model, called GPT-4o, ... OpenAI executives demonstrated a spoken conversation with ChatGPT to get real-time instructions for solving a math problem, to tell a bedtime story and to get ...

6. List of unsolved problems in mathematics - Wikipedia

   en.wikipedia.org/wiki/List_of_unsolved_problems...

   Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

7. Simulated annealing - Wikipedia

   en.wikipedia.org/wiki/Simulated_annealing

   Simulated annealing. Simulated annealing can be used to solve combinatorial problems. Here it is applied to the travelling salesman problem to minimize the length of a route that connects all 125 points. Travelling salesman problem in 3D for 120 points solved with simulated annealing. Simulated annealing ( SA) is a probabilistic technique for ...

8. Cramer's rule - Wikipedia

   en.wikipedia.org/wiki/Cramer's_rule

   Cramer's rule. In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one ...

9. OpenAI - Wikipedia

   en.wikipedia.org/wiki/OpenAI

   OpenAI also makes GPT-4 available to a select group of applicants through their GPT-4 API waitlist; [240] after being accepted, an additional fee of US$0.03 per 1000 tokens in the initial text provided to the model ("prompt"), and US$0.06 per 1000 tokens that the model generates ("completion"), is charged for access to the version of the model ...