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Neuromorphic computing has the potential to accelerate high performance parallel and low power in-memory computation, artificial intelligence, and adaptive learning. Despite emulating the basic functions of biological synapses well, the existing artificial electronic synaptic devices have yet to match the softness, robustness, and ultralow power consumption of the brain. Here, we demonstrate an all-inorganic flexible artificial synapse enabled by a ferroelectric field effect transistor based on mica. The device not only exhibits excellent electrical pulse modulated conductance updating for synaptic functions but also shows remarkable mechanical flexibility and high temperature reliability, making robust neuromorphic computation possible under external disturbances such as stress and heating. Based on its linear, repeatable, and stable long-term plasticity, we simulate an artificial neural network for the Modified National Institute of Standards and Technology handwritten digit recognition with an accuracy of 94.4%. This work provides a promising way to enable flexible, low-power, robust, and highly efficient neuromorphic computation that mimics the brain.