The Alan Turing Building, completed in 2007, has been designed by the well-known firm of architects Sheppard Robson, who have taken pains to incorporate the ideas and suggestions of many of the School's staff and students. The School of Mathematics accommodation consists of two east-west fingers of three floors each, separated by a spacious atrium and connected at either end by open bridges to encourage circulation. The building is named after Alan Turing, who was a Reader in Mathematics at Manchester, and is regarded as one of the founders of computer science. The building also houses the Photon Science Institute and the Jodrell Bank Centre for Astrophysics.

The atrium houses a small cafe (Pi in the Sky) and provides access to the ground floor facilities. These include small and medium sized teaching rooms, undergraduate work and common rooms, a large computer cluster, and administrative support for undergraduate students. The atrium hosts events ranging from local outreach to visiting days for applicants and welcoming parents to graduation celebrations.