Irreligious theism

Irreligious theism is the belief that there is a higher being, but doesn't follow organized religion, this belief can be often confused for deism, however irreligious theists often believe that god can still interfere in the world, also irreligious theists believe in supernatural events like miracles, while deists don't believe in that.
Famous irreligious theists from history include Austrian-American mathematician, logician, and philosopher Kurt Gödel, and American author Martin Gardner.