Peter Tennant Johnstone (born December 28, 1948) is Professor of the Foundations of Mathematics at the University of Cambridge, and a fellow of St. John's College.

His thesis, completed at the University of Cambridge in 1974, was entitled "Some Aspects of Internal Category Theory in an Elementary Topos".

[3] Peter Johnstone is a choral singer, having sung for over thirty years with the Cambridge University Musical Society and since 2004 with the (London) Bach Choir.

Following a severe bout of COVID-19 in 2020, he was invited by the Bach Choir's musical director David Hill to provide the text for a new choral work about the pandemic which the Choir commissioned from the composer Richard Blackford; the piece, `Vision of a Garden', was performed at the Bach Choir's first post-lockdown concert in October 2021 in the Royal Festival Hall, london, and again in July 2023 in King's College Chapel, Cambridge.

[4] He is a great-great-great nephew of the Reverend George Gilfillan who was eulogised in William McGonagall's first poem.