Define “useless”. Many pure mathematicians wouldn’t call their work useless, but also don’t care about its application to the ‘real’ world. G.H. Hardy (https://

Define “useless”. Many pure mathematicians wouldn’t call their work useless, but also don’t care about its application to the ‘real’ world. G.H. Hardy (https://en.wikipedia.org/wiki/G._H._Hardy https://en.wikipedia.org/wiki/G._H._Hardy): “I have never done anything "useful". No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” He also wrote: “It is never worth a first-class man's time to express a majority opinion. By definition, there are plenty of others to do that.”