Doubt as a Key to Mathematical Knowledge

In my arabic culture, doubt, especially when directed at supperiors, is considered extremely disrespectful. In contrast the proverb, “Doubt is the key to knowledge” indicates that doubt should be looked at in a positive light and specifically as a way of knowing. However doubt is unable to be associated as a way of knowing as it is an emotion. It is a feeling that is associated with a lack of conviction in knowledge and therefor causes us to seek further knowledge. However doubt can be integrated differently in contrasting areas of knowledge such as mathematics and religion.

Mathematics is an area of knowledge which is only corned with reason. Certain mathematical formulas is tool with which we use to navigate the mathematical world. A mathematical formula such as the pythagorean theorem formula a2+b2=c2leads us to an answer of the longest side of the triangle, the hypotenuse. There is no alternative to the answer or personal interpretations to the answer which we receive from this formula, it is either right or wrong.

This is because the main way of knowing, evidence and reason, is required to know if a mathematical statement is true or false. When I was first introduced to the idea of absolute value it did not make sense to me. How could a number that was negative equate to the value of its positive counterpart. In my mind, it seemed counterintuitive to create a mathematical number system with negative numbers if negatives was being negated through absolute value.

This caused me to be both confused and curios. Either the previous mathematical information about negative numbers was wrong or the new information about absolute value was wrong. But my mathematics teacher then explained the concept of a number line, which showed that both a negative and a positive number could have the same distance from zero. It turns out that both the information I learned before and the new information was right. My doubt was therefore instrumental in my understanding of this knowledge.

On the other hand, the application of mathematics as a school subject has led to doubt being detrimental to my knowledge of mathematics. The school environment has caused an increased competition among students for achieving the best grades. This causes us to prioritize the easiest and fastest ways to retrieve information. When ever I am doubtful of a mathematical concept I usually ask my teacher for clarification. When solving mathematical problems alone however I have an increased tendency to directly look at the answers in the back of my book when I am stuck on a particular problem or concept.

There was therefore a dependence on my math teacher or the textbook in providing me with answers to my problems. This caused me to always verify my answers with an authoritative source either my teacher or the textbook, and caused there to be less room for me to explore and develop my own methods in solving these problems being constrained to the way the textbook or my teacher shows the method to the answer. My doubt therefore caused a lack of confidence in my mathematical ability and caused me to be dependent on authoritative sources.