DeepMind's recently introduced 540 billion parameter language model PaLM can already explain complex jokes and and reason logically by explicitly describing reasoning steps. The results are quite impressive. https://ai.googleblog.com/2022/04/pathways-language-model-pa...

To be sure, this happened just two years after GPT-3. So 5 years for something which Gowers wants, but based on a large language model, seems in fact quite realistic.