"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity"

This quote by Alan Turing suggests that mathematical reasoning is a combination of two unique professors, instinct and ingenuity. Intuition is the capability to understand something intuitively, without the need for conscious thinking. It is the capability to recognize patterns and make connections in between ideas without needing to consider them. Resourcefulness is the capability to consider innovative options to problems. It is the capability to come up with ingenious ideas and to discover ways to fix complicated issues.

Turing's quote indicates that mathematical reasoning needs both instinct and ingenuity. Instinct allows us to acknowledge patterns and make connections between concepts, while ingenuity allows us to come up with creative services to problems. Together, these two professors enable us to believe critically and resolve complicated mathematical issues.

Turing's quote likewise recommends that mathematical reasoning is an intricate process that needs both instinct and resourcefulness. It is not enough to simply recognize patterns and make connections in between ideas; one need to also be able to think of creative solutions to issues. This needs a mix of both instinct and ingenuity. Without both of these professors, mathematical reasoning would be difficult.