There is at present no satisfactory general theory of special ruled surfaces, or scrolls, and the main object of this paper is to develop the theory of certain fundamental scrolls from which all special scrolls may be obtained by projection.

He visited Oxford and Cambridge searching for willing and bright recruits. This was a fairly challenging task since, as Denniston noted, "it was naturally at that time impossible to give details of the work" that these recruits would be required to carry out. One recipient of the letters sent out to lecturers at these two universities was Gordon Welchman.

Welchman, assigned by Dillwyn Knox on arrival at Bletchley Park to comparatively low-level research on call signs, quickly realized that he and his few colleagues were dealing with an entire communication system that would serve the needs of the German ground and air forces. It was the development of traffic analysis which was his greatest contribution, but in these early months he made two startling breakthroughs in enabling Enigma-coded signals to be read.

He made lists of anything he believed to be of interest and gradually worked his way through the masses of messages that he had been sent. He was also presented with a very small collection of decoded Enigma messages (no more than three days worth). These he found particularly helpful, as they gave an illustration of the types of messages that the Germans were likely to transmit, the polite manner in which they addressed each other, and the style of their signature at the conclusion of the message, which would always include their full title and name. Furthermore, Welchman realised that a particular design flaw of the Enigma machine meant that a letter could never be encrypted as itself. He further realised that if A was encrypted as B for example, then B would be encrypted as A. This was massively important as it reduced the number of combinations of encryptions significantly.

... help some students to appreciate the volumes on 'Principles of Geometry' by Professor H F Baker.

This is a treatise on algebraic projective geometry of the plane with extensions to higher dimensions. Designed as an introduction to more advanced work, the author applies "to the more elementary problems the types of reasoning that are used in advanced work." ... The book is well written, the expositions clear and ample. The printing is excellent and the formulas well displayed. The methods are almost entirely algebraic except for a few synthetic proofs ...

... provides services in systems analysis, systems engineering and technical direction for U.S. Government Agencies and other public-interest organisations.

Amongst other things, Welchman was involved in investigating the optimum design of battle field communication systems and found that many parallels could be drawn with his work at Bletchley Park, despite how great the advancements in technology had been in the years in between.

That was the first book which actually explained how they did it. All the other books told the story about Bletchley Park, the fact that messages were decrypted on an industrial scale and all this intelligence was produced, there was lots of information about how it affected the outcome of World War Two, but nobody was allowed to or dared describe the process of how they actually did it. Welchman's book was the first and interestingly enough it probably remains the only serious book in print to describe technically how the Bombe worked and how Enigma messages were decrypted on an industrial scale. There were references to it in other books but not in the detail that Welchman went into.

A book entitled "The Hut Six Story", by Gordon Welchman, has been published in the United States and is due for publication in this country in June. Welchman was in charge of Hut 6 at Bletchley Park during the first part of the War. Hut 6 was responsible for the cryptanalysis of German Enigma traffic. The book goes into very considerable technical detail about the method developed for this work. Much of the information in the book is still classified in both the United Kingdom and the United States. Little World War II cryptanalysis information is directly relevant to present day exploitation. None of the revelations are directly damaging to UKUSA Sigint. There must however be some indirect damage, in the sense that so long as Signet and cryptanalysis are kept in the public eye by books of this sort, foreign COMSEC organisations will receive more funds and will be stimulated to greater efforts.

He became an American citizen in the early 1960s so he thought he was immune from prosecution. He knew that GCHQ weren't keen and that if he asked GCHQ they would say no. But he had other reasons for wanting to do it. It wasn't an ego trip and it wasn't about making a lot of money. ... He was 33 at the beginning of the war and, by Bletchley Park standards, that was middle aged. They were all so young. He'd recruited a lot of former students and he found some of his colleagues, had almost been disowned by their families. He just felt their story should be told and even if he didn't name or quote them, people would be more aware of the amazing things these people did. Welchman encountered suspicion himself, from his wife's family, who were senior military figures. They saw him out of uniform, at the age of 33, and Welchman was not able to tell them what contribution he was making to the war effort.

In his prologue to The Hut Six Story Welchman says that the lessons that should be taken from his story are firstly that protection against theft, enemy infiltration, sabotage and so on are just as important as protection against the enemy breaking your own codes. Secondly, he makes the point that studying the flaws in the use of the Enigma machine that he himself exploited highlights the importance of adequate training and monitoring of all those who work within the system of battle field communications. He emphasises the lesson that can be learned of the importance of close cooperation between military sectors. Lastly, and most importantly, he stresses that those in charge of current day security systems must remain mindful of future technological advancements in the present day. He believed that there was an important warning in the fact that the Germans believed the Enigma code to be entirely unbreakable and therefore put far too much faith in its insusceptibility to enemy cryptanalysis. They had not planned for the invention of the bombe, a brand new electromechanical device.

Welchman had an acute analytical mind, boundless drive and enthusiasm, but rather limited imagination. At a crucial moment in the Second World War he brought together discrete ideas and divergent pieces of evidence to produce a total policy framework. As a man, though not always easy for his colleagues to communicate with, he was admired, trusted, and liked, for his great charm as well as intelligence and kindness. ... He loved mountains, for climbing and skiing. He was an avid gardener and a keen amateur musician.