This is the title of a talk I gave on 23rd January, 2004, at the
Cambridge University Society for the Philosophy of Mathematics.
This is an excellent seminar run by students and attended by both
philosophers and mathematicians of all levels, from undergraduate up to
professor. The format is: a 45 minute talk followed by 45 minutes
of invariably lively discussion (which usually spills into the
A source of tension between Philosophers of Mathematics and
is the fact that each group feels ignored by the other; daily
practice seems barely affected by the questions the Philosophers are
considering. In this talk I will describe an issue that does have an
impact on mathematical practice, and a philosophical stance on
mathematics that is detectable in the work of practising mathematicians.
No doubt controversially, I will call this issue 'morality', but the
is not of my coining: there are mathematicians across the world who use
the word 'morally' to great effect in private, and I propose that there
should be a public theory of what they mean by this. The issue
arises because proofs, despite being revered as the backbone of
mathematical truth, often contribute very little to a mathematician's
understanding. 'Moral' considerations, however, contribute a great
deal. I will first describe what these 'moral'
considerations might be, and why mathematicians have appropriated the
'morality' for this notion. However, not all mathematicians are
with such notions, and I will give a characterisation of 'moralist'
and 'moralist' mathematicians, and discuss the development of
in individuals and in mathematics as a whole. Finally, I will
a theory for standardising or universalising a system of mathematical
and discuss how this might help in the development of good mathematics.
I have written this up and incorporated my slides into the text.
is available in pdf: click here