Jasper Dale Skinner II

When I first became seriously interested in Squared Squares, back around the year 2000, I was surprised that there was no place on the internet where one could go and access all the information and discoveries concerning squared squares and squared rectangles. As a graduate of Sydney University I was able to get a library card and access mathematics publications databases. I collected as much information as I could on the topic, and was able to understand the electrical network method of creating squared rectangles and had some success in writing software to produce them. I also wrote a letter to William Tutte, where I described a way of constructing the p-net of Duijvestijn's order 21 SPSS from the c-nets (and duals) of the order 9 SPSRs, he was interested enough in what I found to write back to me, told me I would need to do more work to determine if my method was viable or just a coincidence (I did do more work and it now seems to have been an unusual coincidence). In his letter to me, Tutte also urged me to get in contact with Jasper Skinner, as he was the foremost researcher into squared squares and squared rectangles at that time. I felt a little unprepared to engage with Skinner, as I was quite the novice and although I had developed some software it was not particularly efficient and had yielded few discoveries. Instead of writing back, I concentrated on improving my software and building a website about squared squares and squared rectangles.

Shortly after I received an email from Jasper Skinner. Tutte had been in touch with him and they had expected me to write. Skinner wanted to know my interest, motivation and plans for research. He had some concerns about what would appear on a website, I was able to gain his trust and support. He provided me with access to his large collection of squared squares and filled me in on much of the history and theory of the subject.

Jasper is a keen letter writer, but seemed less interested in using email than I was, so we were soon engaged in a regular written correspondence about our mutual interest in squared squares. I soon discovered that Tutte was correct when he named Jasper Skinner as the foremost researcher in this area at the time. Jasper had come to squared squares relatively late, in the early 1990's, but he began making significant discoveries straightaway and was in contact with most of the original researchers, who at the time were nearly all still alive. Those 'originals' included William Tutte, Cedric Smith, Leonard Brooks, Arthur Stone, Chris Bouwkamp, Arie Duijvestijn and Theo (Phil) Willcocks. Skinner also corresponded with John Wilson (one of Tutte's former students) and Geoffrey Morley who both had made squared square discoveries from the 1960s onwards. A number of leading mathematicians also took an interest in Skinners work and purchased copies of his book 'Squared Squares, Who's Who and What's What', including Conway, Knuth, Coxeter and Ron Graham. One of the originals, Pasquale Federico, passed away in 1982. Federico had recorded all known perfect squared square discoveries in a book he kept, "The Red Book". Skinner was given "The Red Book". Skinner wrote to me, "The problem is one with a history and traditions which I respect and carry on, Stuart ... [some personal anecdotes about various mathematicians] ... These are your predecessors Stuart, I for better or worse, am their legacy. In my seven machines are the history and 70 years of humanity's endeavour on this and several allied problems. With a database of nearly 12,000 perfect squared squares [mostly] orders 21-30."

In the months that followed, Jasper wrote and mentored me on a range of topics concerned with squared squares and squared rectangles. Many of the topics I had never heard of. According to Jasper much of the research on squared squares has never been published, or if it has, the most recent results have not been made publically available.

The following topics featured in Jasper's correspondence and will be expanded upon and extended into separate reports