Doubt arose when our thought is between belief and disbelief or feeling of being uncertain about something  . Persian proverb says that doubt is the key to knowledge because from doubt, we have the feeling to know about something new. When we are 100% confident about something that we think is true, then we will never misunderstood the idea that had been brought in the first place. Maybe without doubt, we would never come across the word "evolution" because evolution is about some facts that is due to the feeling of doubt. Knowledge is something that must be justified by empirical evidence, logic, memory or authority  .
"I doubt, therefore I think, therefore I am"  . From the quotation We can deduced that actually doubt can bring us to nearer to the truth and a key to knowledge due to the fact that when we doubt about something it will lead us to think more and more and that will eventually bring us to new findings. History is one of the area of knowing that need doubt most. However, doubt is not necessary applicable in all area of knowledge such as Mathematics.
History is one of the areas of knowledge that requires doubt in order to claim certain thing as a fact or knowledge. History is not just the compilation of the past that is being recorded solely without any research and discussion, but after the facts are being interpreted and analysed into something significant, that is what we called history. Although the process take a long time, but we have to be thankful to historian because they always have doubt in their new findings. Normally, evolution in history supported by scientific evidence such as fossil record. Without supported by scientific evidence or archives, claim made by historian can be considered as myth. Lets us take an example of a history about Piltdown man. For instance, about 100 years ago, a doctor and an amateur paleoantropologist, Charles dawson claimed about their discovery on fossil in England. According to both of them, a jawbone and cranial fragment has been found  belong to human ancestor and as pioneer evidence of human evolution. After that, these specimens was given a name after the collector (Charles Dawson) as Dawson's down-man or in latin name Eonthropus dawson's  . At that time, the excavation made by Charles Dawson and his team was on purpose to find the fossil remains from human ancestor. Most experts agreed that these specimens age about 500 thousand years old and being displayed in museums for more than 40 years and not more than 500 doctoral theses was made. Out of sudden, an American paleoanthropologist Henry Fairfield Osborn said "We have to be reminded over and over again that Nature is full of paradoxes"  . His statement is made based on his own experiences to remind people that those things that we see and expect does not necessary true as we always being fooled by the nature and the most important thing is we does not exist at the time history was made. Sometimes, historian only made a speculation or lucky guess on the specimens they found as long as meeting the theoretical expectations.
At first, some scientist doubt about the specimens was from human ancestor because the skull fragment and the jawbone obviously from two difference species. Due to some limitation at that time such as limited area of study about human evolution and interpretation of fossil, lack of technological equipment to test for the authentication has become the main factors on why Piltdown man remains as a fraud for a long period. To be more precise, perception and reasons of the public toward the Piltdown man has become the major factors that the claimed made is accepted as knowledgeâ€¦â€¦â€¦.(need to add WOK).
Until the new discoveries of new ancient hominids such as peking man and new technologies were discovered and the truth about Piltdown man is revealed. A few attempt made by scientist to prove this claim is wrong. In 1925, one of the scientists named F. H. Edmonds doubted the geological dating made by Darwin. He claimed that the fossil is younger than Darwin had assumed  . After that in 1949, a paleonthologist, Kenneth Oakley from the British Museum Department has tried the technology of flourine testing in order to determine the date of fossils. He applied the technology on the fossil of Piltdown man and fortunately the result was absolutely amazing  . From the test, he found that the Piltdown man fossil is combination of human skull and orang utan. The age of the skull is not more than 500 years. A conclusion is made by paleontologists in July 1953 when international congress was held. Dr. J.S. Weiner concludes that Piltdown man is a join together of a piece of jigsaw puzzle with the right colour but wrong shape  and immediately the specimens was removed from the museum.
From the chronology of the events in order to find the truth about Piltdown man, we found that doubt is crucially important. Now, we can agree that doubt plays an important role in finding the truth. Without this doubt, the fact that the Piltdown man belong to human ancestor will remains until today. A finding will and only will become useful and significant when it is open to an argument. So it can be understood that even an evolutionist will get the closest interpretation on the fossil findings when they doubt and willing to discuss among themselves.
Doubt is less obvious in Mathematics because it is less ambiguous, more clearly defined and less open to interpretation  as math is more to numbers and can be differentiate very clearly which one is wrong and which one is right or in other word the answer is not subjective. Math arise from problems that we face everyday. The solution in Math is based on logical reasoning. To doubt Mathematics is like to doubt why we became a son or daughter to our parents. We have no answer for that and the same thing goes to math. People do not doubt the new discovery in Mathematics due to the ability of self-proving. Instead of doubting, mathematician work on the previous one to expand and search for new axiom. The previous knowledge is still acceptable even though there is a new discovery in math. The simplest example is first and second derivative. The first derivative is found first and after some time only people discovers second derivative. The existence of second derivative never denies or eliminates the first derivative. Math evolves from time to time because not all math problem is applicable toward only 1 axiom. From this, we know that knowledge in Mathematics is expanding not because of doubt, but curiosity.
Albert Einstein stated that " as far as the law of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality" 
From the statement by Persian proverb, doubt is the key to knowledge, we can conclude that not all areas of knowledge is depend on doubt. Although doubt is agreed to be most important thing in order to find knowledge, but it only applicable to certain area of knowledge such as history, art and ethics. In mathematics, doubt doest bring much changes in their evolutionary.