Fionntan Roukema Homepage
Fionntan Roukema

Contact Details

School of Mathematics and Statistics
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
United Kingdom

Telephone: +44 (0)114 222 3872

Email: f.roukema (at)

As a happy young mathematics graduate student

Still happy doing mathematics, but no longer so young...

About me

I am a University Teacher in mathematics at the University of Sheffield. I am a pure mathematician with research interests in low dimensional topology. I am enthusiastic about learning and teaching mathematics; my office is K12 Hicks Building and you should feel welcome to pop in if you would like to chat about mathematics.

As an undergraduate I studied at the University of Edinburgh and the University of California at Berkeley, and as a graduate student I studied at the University of Cambridge, the University of Toronto and at the University of Pisa. I completed my Ph.D. in 2011 under the supervision of Prof. Carlo Petronio and Dr. Bruno Martelli at the University of Pisa. I arrived in Sheffield as a Research/Teaching Associate, developed as a mathematician and teacher, and graduated into a teaching specialist pathway in 2017. 

In addition to mathematics I have passions for travel, wildlife (here's a video I took), good food, good coffee, and good company.



My mathematical interests lie in low dimensional topology. To date all my work has connected to knot theory; I have worked on problems in Dehn surgery and the geometry of 3-manifolds, virtual knot theory, and finite type invariants ((pre)prints can be found here). Since entering the teaching specialist academic pathway in 2017, I have been developing a growing interest in mathematical philosophy, history and pedagogy. 


Teaching and further mathematical engagement

At Sheffield, I've been lucky to have a broad range of teaching. To date, I've led teaching on 14 different modules (foundation year to final year undergraduate, and engineering service teaching to final year specialist modules), designing the curriculum and content for 5 of the modules, and supervised a number of summer research and masters projects across pure mathematics and mathematical communication. I'm currently working on a book which will aim to motivate the university approach to mathematics and whet the appetite for further study. I intend to make resources I have made available here at some point in the future. In the meantime, you can have a look at the best educational resources I've come across online below.

Beyond my formal university teaching, I am passionate about promoting mathematics and widening mathematical participation. Here are some of the ways that I have helped to promote a love for mathematics:   


Further mathematical engagement

I am passionate about promoting mathematics and widening mathematical participation. Here are some of the ways that I have helped to promote a love for mathematics:


Links and brilliant educational resources

My mathematical links are with Benjamin Audoux, Dror Bar-Natan, Bruno Martelli, Ana Lecuona, Louis Leung, and Carlo Petronio. I've collected my favourite online mathematics and education resources below. So, have a look if you'd like to fuel your teaching from primary school to postgraduate levels!

(Hyperbolic manifolds)

SnapPy, written by Marc Culler, Nathan Dunfield and Jeff Weeks, is a wonderful mathematical programme if you are interested in hyperbolic 3-manifolds, and this makes an exceptional addition if you are interested in enumerating all exceptional surgery instructions on a link complement in the 3-sphere. My work has been enormously developed by this software.

(A-level mathematics and secondary schools)

Underground Mathematics, started as the Cambridge Mathematics Education Project in 2012, and I served as the Sheffield correspondent for the project. The final result is a stunningly good collection of teaching resources which should help teachers around the world deliver great classes. I am very pleased to have played an extremely small role in the development.

(Primary Schools)

Play of the Wild is an absolutely beautiful creative educational site with fabulous ideas for teaching early year students mathematics and beyond! My interests in promoting mathematics has taken me to primary schools to do university and research level mathematics! So, I was really happy to come across Play of the Wild.


Disclaimer: Information on this site may be out of date (last updated December 2019).