How did the vast corpus of mathematical innovation of Henri Poincaré (1854–1912) engage the rationale, and impact the fate, of the notion of the ether in physics? Poincaré sought the ‘true relations’ that adhere in the phenomena—relations that persist irrespective of the choice of a metric geometry and a change in physical theory. This chapter traces how Poincaré embedded utterly new geometries and topological intuitions at the heart of pure mathematics, mathematical physics and philosophy. It demonstrates that Poincaré had no ownership of the physicists’ ether concept and that he viewed the ether as neither necessary nor necessarily a hindrance for further advance. Poincaré attended to the profound and subtle needs regarding space and time within physics by creating profound and subtle mathematics to capture the ‘true relations’, of spacetime. Poincaré thereby rendered the physicists’ ether superfluous while also creating mathematical structures for gravitational and quantum phenomena.