At each Annual Meeting of the Australian Mathematical
Society, students compete for the B.H. Neumann prize for
the best student talk presented at the Meeting.
As the judging panel for the 1993 Meeting at the
University of Wollongong we believe that we should set out
the criteria we used for our decision and offer some
guidance for future competitors. Although future judging
panels need not be formally bound by our ideas, we would
expect them to take a similar view. Our judgement was
based on three main criteria: presentation, content and
rapport with the audience.
Talks are about communication and with mathematics,
even amongst mathematicians, this is a formidable
task. The speaker has to keep in mind that diverse
mathematical interests are represented in the audience. So
the introduction can afford to be relatively long. Effort
has to be made to get as many as possible motivated by a
clear simple statement of the problem area.
We have to be realistic about what can be covered and
what an audience can absorb in a half-hour talk. Very
often we get excited about the solution to a problem and
we want to tell about this to the last detail. But be
careful, sometimes great discoveries in the complexity of
a polished generalisation. The audience has a better
chance of catching the excitement of the discovery and
valuing it if they can appreciate the first elemental
insights which led to the completed work. If you catch the
audience's interest then afterwards they will ask for your
paper to pursue the details.
Of course it is important that the talk be well
prepared. If overhead transparencies are used they should
be written with an eye to presentation. There is a
problem with the use of overhead transparencies; they do
detract from the immediacy that a blackboard presentation
can give. Overhead transparencies should have restricted
use as an aid. Spontaneity is not lost if the speaker
spends time talking directly to the audience or using the
blackboard for diagrams, or sketching on the overhead
transparencies. As a rule, no more than six transparencies
should he used for a short talk; these should not contain
densely packed material and, as far as possible, they
should not refer back to statements or equations in
previous transparencies.
Care should he taken to consider how much formal proof
material can reasonably he presented in a half-hour
talk. Perhaps the proof of one key result can he presented
towards the end of the talk. Preferably such a proof
should he given by outline showing how main ideas
interact. Remember, the talk is to communicate and create
interest in the material. The talk is not successful if
the speaker overwhelms the audience with a mass of detail
that they could not possible follow even given a much
longer time.
Mostly the speaker's concern is with the mathematical
content; after all, wrestling with a problem and
organizing its solution has been a consuming
occupation. The judging panel is concerned about the
originality of the material and the speaker's contribution
to the solution. It is important for the speaker, when
setting the problem in context, to list those on whose
work they are building and to explain the role the speaker
played and to mention collaborators. An assessment of the
weight of the contribution and an outline of the problems
which remain are also of value and help the audience gain
some perspective on the depth and relevance of the
work. It is useful to illustrate the material with
examples because this makes the argument more convincing
and is often a point of contact with the audience.
The speaker should try to gauge whether the audience is
following the presentation. Of course, it is difficult to
present complex material in a restricted time and have
concern for audience understanding. Nevertheless, a
successful talk depends on it. Audience interest often
shows itself in questioning during or at the end of the
talk. The judging panel is interested to see how the
speaker handles questions. One of the most fruitful
outcomes of any talk is the building of research
contacts.
Finally, all students preparing to give talks should do
a "dry run" at their home university well before the
conference to a friendly audience containing an
experienced speaker and someone not directly in the field.
From such a preliminary presentation the amount of
material can be checked. This will help to highlight the
key points which should be the focus of the talk. Often
there will he the discovery that many non-essential side
issues will need to be excised to give a clearer
presentation in the short time. Practice is essential in
handling transparencies and and necessary revisions can
be made. A home audience is likely to he more openly
critical and will play a crucial role in advising about
polishing the presentation.
There is a valuable paper written by the master
expositor, Paul Halmos, which should he essential reading
for all postgraduate students. The reference is "How to
talk mathematics'' Notices Amer. Math. Soc. 21 (1974),
155-168.
B.H. Neumann Prize judging panel, 1993.
- John Giles (Newcastle) (Committee Chair)
- Bob Bryce (ANU)
- Mike Englefield (Monash)
- Mike Newman (ANU)