Does the abstract mathematical world exist independently of the physical world? Roger Penrose, the author of "The Road to Reality", regards this as part of the Platonic world — and seems to incline to the view that it does have an independent existence, as some kind of eternal truth. I'd appreciate folk who visit this forum sharing their views on this question with a self-confessed mathematical heathen who thinks that: Mathematics is a language rooted in the fact that descriptions are often more useful when they are made quantitative. For example a man-made tool like the counting numbers (1,2,3,4 ....etc.) helps most folk to be practical. At its most primitive micro-level — arithmetic — the Platonic mathematical world consists of only these numbers and their operations. The complexities of the imagined mathematical world are now of course much, much greater. They have evolved, like the complexities of the similarly intricate world of music. Despite the misgivings of conservative folk over the years, the simple concepts of arithmetic have been hugely elaborated. For example, to start with, number systems have been modified to include useful inventions that aren’t the ratio of two counting numbers (like pi and e); the strange numbers zero and infinity, and negative numbers. And much else has followed, from imaginary numbers to quaternions and on to the wonders of modern mathematics. Some of the simpler abstractions have eased practical tasks like the counting of sheep, land surveying, building pyramids and the bookkeeping of abstract entities like money in the electronic accounts of a bank. But despite the sophistication of mathematics today I would argue that mathematics remains at heart an ephemeral human language that has been developed to satisfy a genetically-coded appetite forced upon us by evolution: a driving need to describe whatever we observe and whatever we can imagine. Neither the abstract constructs of mathematics nor the works of Mozart are part of the physical world. It contains no Pauli spin matrices, Euclidean circles or symphonies. These are constructs devised by human beings to satisfy their own peculiar needs; to devise logical systems, to describe physical phenomena or, in the case of music, to express human emotions. The Platonic mathematical world may manifest itself physically as neural patterns in mortal brains, squiggles on paper, binary digits in transit on the internet or patterns on computer screens. But all these are only patterns laid down on substrates that don't endure, but come and go with the years. I would conclude that the Platonic mathematical world is an ephemeral abstract construct that will perish with humanity in the fullness of time, whereas the physical world is likely to endure a little longer.