The Largest Number Smaller Than Five

Posted by: cwlh on: 26/01/2007

• In: Mathematics
• 7 Comments

A couple of blog entries ago I described the process my co-author and I have been through in publishing our book The Largest Number Smaller Than Five with Lulu. The final stage which we were awaiting at the time of that post was the arrival of the revised book. It arrived, again in under a week, and was deemed to be good, even by the people with normal colour vision. So I pressed the magic button on the Lulu site and made it generally available.

Note that people using that button report that they arrive at the checkout with three items in their basket: two copies of the book at different prices and a download. I’m trying to sort this out with the publisher but in the meantime just delete the more expensive version of the book and the download and proceed to the checkout.

It’s a book for young teenagers about mathematics covering the conventional mathematical symbology as a sort of code to be cracked, groupoids, the continuum hypothesis and the completeness of arithmetic, the validity or otherwise of Reductio ad Absurdum and many similar topics. The book is something of a miscellany but, if it does have an underlying theme then that theme is doubt. I remember as a very young teenager being puzzled by what else there was in mathematics: I could add, subtract, multiply and divide integers and fractions and, apart from making the number bigger and the arithmetic therefore harder (remember children that these were the days before pocket calculators), it was difficult to see how else mathematics could extend. Once one has tackled (as we did continuously in primary school) questions of the type:

If 4 tons 3 cwt 7 lbs 13 oz of a substance cost 23 pounds 16 shillings and 6 pence, what will 5 tons 11 cwt 3 lbs 14 oz cost?

it really is difficult to see what else there could be in mathematics. Today, of course, such problems to be solved without a calculator would rightly be considered child cruelty. So doubt: doubt about the techniques we use in mathematics, doubt about the importance of mathematics, doubt about proofs, doubt about all the answers being in the back of the book and the teacher’s head.

We tried to pull no punches and present the mathematics as it really is rather than in a bowdlerised form and may even have succeeded here and there. In the end we couldn’t avoid some mathematics beyond primary school level but we conveniently collected it all into one chapter so that it could be ignored in one go. There are 50 puzzles ranging from the trivial to the currently unsolved and I’ve more-or-less promised a Fields Medal to anyone who solves the latter.