How big can a number get? Leeds academic’s new book tackles maths at its strangest
Some numbers are so large they cannot be written down, even if the entire universe were turned into a notebook.
That idea sits at the heart of Huge Numbers: A Story of Counting Ambitiously, from 4½ to Fish 7, the latest book by Richard Elwes, Associate Professor of Mathematics at the University of Leeds, and a recent Holgate Session Leader for the London Mathematical Society.
Rather than treating mathematics as a neat collection of formulas and proofs, the book explores it as a centuries-long attempt to describe quantities that stretch beyond ordinary experience. Readers can learn about ancient Egyptian number systems, vast Mayan calendar cycles, and Archimedes’ calculation of how many grains of sand could fit inside the universe.
Alongside these historical detours are examples drawn from modern life. Dr Elwes examines the astronomical figures used in computing, finance, and physics, drawing on historical situations like the hyperinflation of post-war Hungary, and the timescales associated with the evaporation of black holes.
Dr Richard Elwes.
He also explores numbers so extreme they challenge the limits of notation itself, including the googolplex and the even stranger TREE(3), a quantity so enormous that writing it out in full is physically impossible.
The book also highlights how different civilisations approached counting, long before modern science emerged. Jain scholars in India developed theories involving extraordinarily large quantities, while Greek mathematicians invented new vocabularies to discuss values beyond the reach of existing systems.
Rather than being a catalogue of mathematical curiosities, Huge Numbers aims to offer a thorough account of how humans have repeatedly expanded the boundaries of thought; as Dr Elwes argues, large numbers have shaped scientific progress as much as equations or geometry.
Richard Elwes’s new book ‘Huge Numbers’ is great.
He said: “I loved writing Huge Numbers. It gave me the opportunity to dig into many fascinating topics from ancient history to the far future of the universe. I hope readers will enjoy accompanying me on this journey through the biggest numbers that humans have ever contemplated.”
Dr Elwes has taught many subjects at Leeds, including mathematical logic and the history of mathematics, and has written five books before Huge Numbers. You can get your copy of Huge Numbers now from Waterstones and other well-known booksellers for £25; it is also available in e-book and audiobook formats.
