PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
What Do Mathematicians Do When They Have a Proving Impasse?
Page: 1-388
This paper reports what six mathematicians did when they came to impasses while constructing proofs on an unfamiliar topic, from a set of notes, alone, and with unlimited time. Detailed information is given on two of the mathematicians. 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 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 kind relates directly to the ongoing argument, while the other kind consists of doing something unrelated, either mathematical or non-mathematical. Data were collected using technology and a new technique being developed to capture individuals’ autonomous proof constructions in real-time.