Until October 2003 I was a research student at Trinity College and DPMMS, Cambridge. I have done a PhD from 1999 to 2002 and for 2002–3 I had a Senior Rouse Ball Studentship from Trinity; I still sometimes think about unsolved problems and go to Combinatorics Seminars of particular interest (with no official position in the University or a College).

My Erdős number is 3 (Erdős—{Bollobás, Janson, Łuczak, Payan, Schelp}—Thomason—Myers).

My general research area is combinatorics, and most of my research so far has been on extremal problems in graph theory (loosely interpreted). The specific area within this in which I have made the most progress is that of graph minors (though I have also worked on various other problems).

My PhD supervisor was Dr Andrew Thomason. I submitted my PhD dissertation Extremal Theory of Graph Minors and Directed Graphs on 31 October 2002 and passed my viva on 8 January 2003. The award of the degree was then considered by the Degree Committee on 23 January 2003 and approved by the Board of Graduate Studies on 11 February 2003. The degree was conferred at the Congregation of the Regent House held on 22 February 2003.

Details of papers published (generally with abstracts and copies of the papers) or submitted, seminars given, etc., are on my publications and preprints page, which also includes nonacademic work.

There is no general definition of the distinction between ‘serious’ mathematics and recreational mathematics, nor in all cases a clear distinction. Typically the recreational may involve solutions to particular special-case problems with no ‘interesting’ generalisations, or the generation of examples with no particular underlying theory, or ideas without many links to the rest of mathematics, while the serious may involve deeper ideas, generalisations and links to other mathematics, but problems of a recreational nature may have links to deeper mathematics, and generating all the examples with some property may be mathematically hard but of no significance, while problems couched in serious terms and with complicated solutions may turn out to be so specialised that neither the problems nor the solutions are of any wider interest. Hardy’s A Mathematician’s Apology discusses the nature of serious mathematics in much greater depth.

Thus, the distinction followed here is to some extent arbitrary, but contributing factors are the generation of examples without underlying theory, the special-case or trivial nature of the problems, and not being published in academic journals.

- I construct card models of polyhedra.
- I analyse various more or less mathematical problems and structures by computer; some results may be linked to below, and some may be in contributions to the On-Line Encyclopedia of Integer Sequences (of which I am one of the associate editors). My research also involves some such analyses, of more ‘serious’ problems. I formerly ran some large computations in parallel across most of the computers in DPMMS.
- Information about tiling the plane with polyominoes, polyiamonds, polyhexes and polykites.
- Recreational publications.

I have been involved in various ways in Mathematical Olympiads since 1992, as a contestant while at school and subsequently helping in various ways with training the next generations of contestants and other activities.

After correspondence training from Tony Gardiner starting in 1992 (and competing in the IIIMC in 1993 and the BMO in 1994 and 1995, but never in the NMC) I was on the UK International Mathematical Olympiad team in 1994 (Hong Kong) and 1995 (Canada). Under the training arrangements then in operation, those teams were also at the first two Summer Schools, at The Queen’s College, Oxford, which doubled as pre-IMO training for the IMO team.

Subsequently I have helped with various aspects of Olympiads and training:

- I have helped at some Trinity training camps (2001 onwards), giving sessions on Algebra and Combinatorial Number Theory in 2005, on Algebra and Combinatorics in 2006, on Graph Theory and Combinatorics in 2007, on Combinatorial Number Theory and Number Theory in 2008, on Combinatorics in 2009 and 2010, on Combinatorics and Algebra in 2011, on Combinatorics in 2012, on Combinatorics and Algebra in 2013, on Combinatorial Number Theory and Combinatorics in 2014, and on Combinatorics in 2015, 2016 and 2017, and have done FST/TST marking from 2002 onwards, as well as chairing the Background Problems presentations in 2008 when David Monk was unable to be present.
- I gave a session on Combinatorics at the Oundle camp in 2005, a Ramsey Theory session and an Algebra shortlist session in 2006, a session on fallacious proofs and shortlist problems in 2007, a session on Combinatorial Geometry in 2008, a Combinatorics session in 2009, a session on fallacious proofs in 2010, an Enumerative Combinatorics session in 2011, a Combinatorics session in 2012, a Number Theory session in 2013, an Enumerative Combinatorics session in 2014, a Combinatorial Geometry session at that camp (moved to Tonbridge) in 2015, a fallacious proofs session in 2016, and a talk on ‘Why Geometry is Boring’ in 2017, as well as doing NST/TST marking from 2006 onwards.
- I have been a mentor on the Senior Mentoring Scheme (2001, 2002), the Advanced Mentoring Scheme (from 2003 onwards) and the special EGMO Mentoring Scheme (Summer 2011) (and have otherwise assisted students in mathematical correspondence outside the Mentoring Schemes).
- I have done BMO1 marking from 2004 onwards, BMO2 marking from 2007 onwards, and IMOK Olympiad (Maclaurin) marking from 2011 onwards (but not in 2014 or 2015), as well as UK MOG marking from 2011 onwards.
- I was a Coordinator on Problem 3 at IMO 2002 in Glasgow, on Problem 4 at EGMO 2012 in Cambridge, on Problem 6 at EGMO 2013 in Luxembourg, on Problem 5 at EGMO 2014 in Antalya, on Problem 6 at IMO 2014 in Cape Town, on Problem 5 at EGMO 2015 in Minsk, on Problem 1 at IMO 2015 in Chiang Mai, on Problem 6 at EGMO 2016 in Bușteni, on Problem 3 at IMO 2016 in Hong Kong, on Problem 3 at EGMO 2017 in Zürich, on Problem 3 at IMO 2017 in Rio de Janeiro, on Problem 4 at IMO 2018 in Cluj-Napoca, on Problem 3 at IMO 2019 in Bath, on Problem 3 at the virtual IMO 2020, on Problem 5 at the virtual IMO 2021, on Problem 5 at EGMO 2022 in Eger, on Problem 1 at IMO 2022 in Oslo, and on Problem 5 at IMO 2023 in Chiba. I was also Chair of the Problem Selection Committee at IMO 2019.
- I was an Observer with Leader with the UK delegation at IMO 2006 and the pre-IMO joint UK/Slovenia training camp held at Bled, and again with the UK delegation at IMO 2007 in Vietnam and the pre-IMO training in Australia (including assisting with the Coordination of the Vietnamese scripts on Problem 5, a UK submission, in 2007). I also helped at the pre-IMO joint UK/Australia training camps in Cambridge in 2009 and 2011, but did not attend those IMOs. I was again an Observer with Leader with the UK delegation at IMO 2010 in Kazakhstan. At IMO 2023 I was one of five people registered as UK Observers with Leader and acting as Coordinators.
- As well as being a Coordinator at EGMO 2012 I was also a member of the organising committee and of the Problem Selection Committee and generally responsible for EGMO 2012 IT; I also helped with IT at subsequent EGMOs. The software used for EGMO is available for use by other competitions.

Since 1996 I have maintained the UK IMO Register, a listing of the details of past UK team members in the International Mathematical Olympiad. Since February 2003 I have maintained the web site for the British Mathematical Olympiad Subtrust (BMOS) and Committee (BMOC), and since September 2010 I have been a member of BMOC; since October 2013 I have been a member of BMOS. I also maintain the web sites for the European Girls’ Mathematical Olympiad and EGMO 2012.

I was also involved with the film *X + Y*.

See also notes on some individual olympiad problems and other olympiad-related notes.

Return to my home page

Contact: Joseph Myers (jsm@polyomino.org.uk)

Last updated: 11 July 2023