PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
What do mathematicians do when they reach a proving impasse?
Page: 2-532
I report how two mathematicians came to impasses while constructing proofs on an unfamiliar topic, from a set of notes, alone, and with unlimited time. By an impasse, I mean a period of time during the proving process when a prover feels or recognizes that his or her argument has not been progressing fruitfully and that he or she has no new ideas. What matters is not the length of time but its significance to the prover and his or her awareness thereof. I point out two kinds of actions these mathematicians took to recover from their impasses: one relates directly relates to the ongoing argument, while the other consists of doing something unrelated to the ongoing argument which can be mathematical or non-mathematical. Data were collected using a new technique being developed to capture individuals’ autonomous proof constructions on tablet computers in real-time.