The nice thing about mathematics is that it asks you to invent new ways of thinking. Numbers, percentages, Venn-Diagramms, infinite series etc. have accompanied us at school. The story is far from finished. Under there is a nice introduction to the new theory of numbers, called “condensed mathematics“.  Their lecture notes (pdf-file) are a tough read. My take home message simply is, the invention of new approaches to old problems, providing more general answers and/or unifying different fields are particularly rewarding. Maths is a fascinating discipline. You study abstract problems, hardly anybody else has had so far, but you are not considered strange as for example some artists at times. Imagine your new world in music, painting or the arts in more general terms or try to become a mathematician. Finding ways to communicate about your predilection and invention is the next challenge. Many scientist, inventors or artists found very few people to talk to about their new stuff. The internet and social media have changed this. Persons with interests or findings beyond the mainstream find colleagues in other parts of the world. Lighthouses from far away become visible through this. Navigation of other possible worlds turns into reality. These specialisations might turn out to be generalisations. The stretch between indepth knowledge and the polymath approach shall accompany us for a long time. Unified theories in several fields are indeed a step to be able to have an oversight about several, but not all fields. Polymaths probably start with condensed maths to move on to other fields of imagination. There is always a risk to get stuck somewhere on the road in a topological space.