Intuition is one of the eight ways of knowing and maths is one of the areas of knowledge. Therefore, bearing this in mind, we can use intuition to gain knowledge in maths. But, is intuition always a liable way of knowing? Let’s have a look at the Monty Hall paradox to answer this question:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
The contestant should switch to the other door in order to have more possibilities of winning. Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance.
The given probabilities depend on specific assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 that was not available at the beginning of the game, when the door 1 was chosen by the player: the host’s deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally. Another insight is that switching doors is a different action than choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities.
The problem is a paradox of the veridical type, because the correct result (you should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true¹.
In conclusion, intuition is not a liable way of knowing regarding the area of maths as reason can prove it wrong in some cases as the one we have studied. Therefore, we should not use intuition as a way of knowing in maths.
¹En.wikipedia.org. (2017). Monty Hall problem. [online] Available at: https://en.wikipedia.org/wiki/Monty_Hall_problem [Accessed 25 Apr. 2017].