Neural networks in the brain are structured in three-dimensional (3-D) space, and the networks evolve through development and learning, whereas two-dimensional (2-D) crossbars have essentially been optimized for a fully connected neural network, which results in a significant increase in unused memristors. Here, we present a prototype of molecular neural networks on wetware consisting of a space-free synaptic medium immersed in monomer solution. In the medium, conductive polymer wires are grown between multiple electrodes through learning only when necessary, i.e., no polymer wire is pre-placed, unlike present 2-D crossbar devices.Through experiments, we found the necessary growth conditions for synaptic polymer wires.We first demonstrated the learning of simple Boolean functions and then data-encoding tasks by using our system comprising the synaptic media and their external controllers. These results are valuable for expanding the concept of space-free synapse development, i.e., extending our 2-D synaptic media to 3-D is possible in principle.