RUME 25
2023
Omaha, Nebraska
Why Mathematicians ‘Fully Understand’: An Exploration of Influences on Their Understanding
Page: 1104
One of the primary mathematical practices of many professional research mathematicians is engaging with highly advanced mathematical concepts in their research. As mathematicians engage with these concepts in their work, they may or may not ‘fully understand’ them, which could include not being able to deduce why each step in a proof logically follows from the next. This preliminary study investigates what reasons professional mathematicians give for not ‘fully understanding’ mathematical concepts in their own work. One mathematician researching coding theory was interviewed, which utilized one of the participant’s own research journal articles as a launching point for discussion. Various reasons for the participant’s conceived amount of understanding were observed, including authoritative reasoning and academic pressures. Implications for future research on professional mathematicians are discussed.