After graduating from Cambridge University, Rowbottom studied under Howard Jerome Keisler at the University of Wisconsin–Madison, earning his Ph.D. degree in 1964, with a thesis entitled Large Cardinals and Small Constructible Sets, under the supervision of Jerome Keisler. With a recommendation from Georg Kreisel, he took a position at the University of Bristol in 1965, where he spent the rest of his professional career.
He published a paper called "Some strong axioms of infinity incompatible with the axiom of constructibility" in the Annals of Mathematical Logic, 3 1971. This paper, together with his thesis, "showed that Ramsey cardinals were weaker than measurable cardinals, and that their existence implied the constructible real continuum was countable; he further proved that this followed also from weaker partition and two cardinal properties." The large cardinal notion of Rowbottom cardinals is named after him, as is the notion of a Rowbottom ultrafilter.
Keith Devlin studied set theory under Rowbottom. In 1992 he and a student, Jonathan Chapman, wrote a textbook on topos theory, Relative Category Theory and Geometric Morphisms: A Logical Approach, published in Oxford Logic Guides, No. 16. Rowbottom retired in 1993 at the age of 55.
- Frederick Rowbottom at the Mathematics Genealogy Project.
- In Memoriam: Frederick Rowbottom, "Notices", Bulletin of Symbolic Logic 16 (2), 2010: 299.
- Tryba, Jan (1981), "A few remarks on Rowbottom cardinals", Israel Journal of Mathematics 40 (3–4): 193–196, doi:10.1007/BF02761361.
- Feng, Qi (1987), "On the Rowbottom M-ultrafilters", Journal of Symbolic Logic 52 (4): 990–993, JSTOR 2273832.
- Rowbottom, Frederick and Jonathan Chapman. Relative Category Theory and Geometric Morphisms: A Logical Approach, published in Oxford Logic Guides, Oxford University Press, 1992, ISBN 978-0-19-853434-1
- Review by Colin McLarty (1994), Modern Logic 4 (3): 345–348.
- Review by Ieke Moerdijk (1995), Journal of Symbolic Logic 60 (2): 694–695.