I built a feed forward neural network from scratch, and trained in on the MNIST dataset
After 15 epochs, the network was able to correctly label 98% of handwriten digits that it had never seen before (validation accuracy) with only 1% overfitting.
In the future I would like to explore convolutional neural networks, as they are a quicker architecture. Currently my network is slow (although I'm not sure how it compares to others of its type in terms of speed), so finding ways to improve efficiency is a major goal in the future.