was historically. In the 1960s, many mathematics departments were housed in high-rise buildings including the Mathematics Tower at the Victoria University of Manchester, and the Maths and Social Sciences Building at UMIST. These proved completely unsuited to the activities of a mathematics department (and arguably any academic department) as travel between floors in lifts (and uninviting stairways) discourages interaction between mathematicians resulting from chance encounter. Buildings such as the Mathematics Institute at Warwick (at East Site and later the Zeeman Building) and the Isaac Newton Institute at Cambridge are deliberately low-rise and designed to encourage chance encounters. The Alan Turing Building was designed with substantial input from the mathematicians, and the design reflects this including a large open-plan common room on the atrium bridge, open corridors and walkways and the relocation of the best traditional blackboards from the old buildings. Occupancy and facilities The Photon Science Institute occupies the southernmost finger, with the northern two fingers housing Mathematics on the first three floors and the JBCA on the third and fourth floors. The ground floor atrium constitutes a public space including a small café called Pi in the Sky. Surrounding the atrium on the ground floor are the undergraduate common room for mathematics, as well as lecture rooms and undergraduate computer rooms. The first and second floor of the first two fingers mainly house the offices of academic staff and postgraduate students in mathematics, as well as the Manchester Institute for Mathematical Science (MIMS) conference areas. One of seminar rooms is named after the topologist Frank Adams, and the library after algebraist Brian Hartley. Lecture theatres are named after Mordell, Richardson, Max Newman and Lighthill. A meeting room is named after Horace Lamb and the Access Grid room after Sydney Goldstein. The bridge across the atrium is the common room for mathematics academics and graduate students, where morning coffee is served. The third floor houses the academic offices of the JBCA, which provides a new base for the research activities in astronomy and astrophysics with the relocation of many staff and students from Jodrell Bank Observatory. The Observatory now forms part of the JBCA and provides leading observational facilities such as the Lovell Telescope and the Multi-Element Radio Linked Interferometer Network (MERLIN). This floor differs in design from the others in that the rooms have windows onto the atrium and glass walls to central corridors in each wing, whilst retaining