This paper investigates the feasibility of machine learning (ML)-based pilotless spatial multiplexing in multiple-input and multiple-output (MIMO) communication systems. Especially, it is shown that by training the transmitter and receiver jointly, the transmitter can learn such constellation shapes for the spatial streams which facilitate completely blind separation and detection by the simultaneously learned receiver. To the best of our knowledge, this is the first time ML-based spatial multiplexing without channel estimation pilots is demonstrated. The results show that the learned pilotless scheme can outperform a conventional pilot-based system by as much as 15-20% in terms of spectral efficiency, depending on the modulation order and signal-to-noise ratio.