Human memory plays a constitutive role in at least three mathematical activities:
- During the following of an argument, of a proof, one has to remember if not every so at least a certain number of steps in order to be able to see that a connection between certain mathematical items is established by the proof.
- More interesting is the role of memory in making analogies or comparisons between mathematical items which can lead to the statement of questions, problems, conjectures or hypotheses.
- The previous point can be expanded to the activity of finding arguments in order to answer a question, to solve a problem. If the argument is new, maybe there is no memory needed but in most cases an already known argument is borrowed (because it seems to fit the structure of the problem) and maybe modified (or the problem is modified in order to fit the argument). Nevertheless the argument (or technique) has to be retrieved from ones memory.
A last point concerns the relation between memory and habit, between memory and know-how. Maybe it is similar to the relation between memory and spoken language. It seems that the main issue is the time of retrieval of ‘information’ and probably ‘information’ is the wrong word, but anyhow it seems that this retrieval-time is minimized to something we call an ‘instantaneous reaction’. It would be interesting to project this to computers – it seems not to work, since there is always a ‘process’ of information retrieval from the memory (of the computer) which seems not to exist in what we consider to be an instantaneous reaction, something like ‘real-time-thinking’ (this last expression is maybe a pleonasm).