MLX Swift is Apple's open-source numerical computing framework that brings NumPy-style array operations to Swift with automatic GPU execution and lazy evaluation. The session walks through three practical examples: computing the Mandelbrot set using parallel array operations instead of scalar loops, solving heat distribution with Jacobi and Successive Over-Relaxation (SOR) iterations using conv2d, and curve fitting via gradient descent with automatic differentiation. MLX Swift supports the full numerical toolkit including linear algebra, FFTs, convolutions, and optimization algorithms like SGD and Adam. It shares concepts with Python, C++, and C front-ends, enabling prototyping in Python and shipping in Swift. The entire ecosystem is open source under MIT license and installable via Swift Package Manager.