Title: How we discovered Deep Neural Networks at Middlesex University in 2007. Abstract We represent neural networks by directed graphs and consider the problem of maximal connectivity with constraints. This problem is motivated by some conflicting objectives in the design of biological neural networks. One of the solutions of this optimisation problem of neural network with constrains was presented at IJCNN 2007 and resembles what is now called a concolutional deep-learning neural networks. Inequalities and equations derived are tested on data and numerical estimates for parameters of a human brain. Results support an intuition that human brain is maximally connected subject to constraints on in- and out-degrees.