“The more we know, the more we know we know nothing” written by Plato and said by Socrates. Plato expressed the same idea as Goethe which is “with knowledge doubt increases”. The claim expressed by Goethe assumes that when we know less, we tend to have strong beliefs about the certainty of our knowledge, which suggests that confidence may indicate ignorance. This implies that he believed that knowledge is in a state of constant flux, the more we know the greater chance that some of our knowledge will have changed. This is because the limits of knowledge are possibly infinite. As knowledge grows, doubt grows in two directions, a greater awareness of things we don’t know, and a greater level of depth of curiosity into the things we do know. Although,  it is possible to know a lot confidently and that doubt doesn’t necessarily increase with quantity of knowledge. For example, in natural sciences, there is a specific methodology which can eliminate doubt by gathering data, conducting experiments and more. In mathematics, there is also a certain methodology of logical reasoning, which aids mathematicians to deepen their knowledge and also remove doubt,  so they are able to know a lot confidently. In natural sciences, there have been several cases of people who know a lot and have very little doubts in their knowledge, doubts so small that it is safe to say that they know it confidently. Scientists are confident about their knowledge because they acquire it mainly through sense perception, such as sight, touch, smell or hearing. In a scientific method, according to the traditional approach (inductivism), scientists first observe what is happening in an experiment to formulate a hypothesis and once they have results, they develop a theory. To get from the observation to the hypothesis to the theory, they also use reason. Reason gives evidence to our senses which inevitably gives us certainty. For example, the scientist Benjamin Jesty noticed that people who handled cows and had cowpox were not contracting smallpox. He gathered this observation and evidence and then became confident that injecting a cowpox vaccine would mean that people would not get smallpox, which was a much more dangerous disease. He showed confidence in the vast amount of knowledge he gathered by injecting the cowpox virus on to his own children and wife. His family was exposed to smallpox several times throughout their lives and never contracted it, proving that Jesty was right, which he was confident about all along.  In comparison, contemporaries of his were very doubtful of this method, in spite of knowing very little about the concept of vaccines in the 18th century. (“The First Recorded Smallpox Vaccination.”) It can be safe to assume that their doubt was based on ignorance. This is because, nowadays, we know that vaccines work as people who get vaccinated don’t get the respective diseases, which eliminates doubt that vaccines do not work. Jesty used the methodology in natural sciences by observing, collecting evidence and using reason, which removed doubt that the vaccines wouldn’t succeed. In current times, the science of vaccines is quite advanced and we have a strong knowledge with masses of confidence.  Goethe believed that as knowledge grows, doubts also grows. Doubt can grow in two directions, in the ‘known unknowns’, meaning that we will be more aware of what we do not know, or it can grow in the ‘known knowns’, where we start to question what we already know. When we doubt the ‘known knowns’ or the ‘known unknowns’, we attempt to find answers by using intuition. If our intuitions are based on relevant experiences, confirmed by reason and other people’s intuitions, it makes sense to trust them. Once we trust knowledge, doubt may naturally increase. For example, it is true that in current times, scientists are confident and have a strong knowledge on the science of vaccines. This is because they used their intuition by thinking that if smallpox can be avoided by vaccination, then there are other diseases that can also be prevented. This was confirmed by reason because Benjamin Jesty was confident in his knowledge that injecting cowpox would prevent people from contracting the deadly virus called smallpox, which turned out to be true. This true knowledge of ‘known knowns’ came with doubts and with this information scientists started to question why and how, which resulted in the vast amount of information that we now know about vaccines. Even though Jesty was confident in his knowledge, if we treat the cowpox vaccine as a small amount of knowledge, we can see how a whole new branch of science was created. The explosion of virus exploration started, so doubt also started to arise. Since then, scientists questioned what other diseases could be prevented by the use of vaccines. Even today, there are still doubts about the science of immunisation. Doubt does not necessarily increase with quantity of knowledge, meaning that it can be assumed that confidence does not decrease with the more knowledge that we have. Mathematicians can have confidence in their maths as they use a formal system that starts with axioms and deductive reasoning, which can prove theorems. Furthermore, maths uses truth and validity. Logic is useful to preserve the truth and deductive reasoning is useful to reason validity, so this can prove immediate evidence. With this, we can assume that logical reasoning cannot be doubted, as it is based on the law of identity, the law of non-contradiction and the law of the excluded middle. Mathematicians, through their methodology using reasoning and logic, have proved that the Fibonacci spiral can make the most aesthetically pleasing compositions. I wrote my maths internal assessment about the spiral and the equation for creating it is “r=a eb” (Weisstein, “Logarithmic Spiral”). Mathematicians believe that it can create the most beautiful photograph if the ratio is followed, because it was proved through evidence gathered “from Leonardo da Vinci to Le Corbusier, the golden ratio is believed to have guided artists and architects over the centuries.”. “The human eye is capable of interpreting an image featuring the golden ratio faster than any other.” which is “the reason why it pleases the eye” (McVeigh,”Why Golden Ratio Pleases the Eye: US Academic Says He Knows Art Secret.”). Because of all the surveys, experiments and proofs gathered, currently, mathematicians have a strong knowledge and confidence that the Fibonacci Spiral is considered to be the ratio used to make the most aesthetically pleasing composition, due to reasoning and logic.However, knowledge seems to be in a state of constant flux, which is what Goethe seemed to be implying as he said “with knowledge doubt increases”. The more we know the greater chance that some of our knowledge will have changed.  It does not seem likely but mathematics does not give certainty. A conjecture is a hypothesis that does in fact seem to work but it can never be proven to be true. We cannot say that a proposition is true until we have tested every single number possible, and currently we do not have the ability to test every single number because there are infinite numbers.  There is doubt and if we ever become more certain, it may change our knowledge. It is possible that maybe one day we will find a contradiction, even if it is a small contradiction in a formal system, it could possibly change the entire system. For example, currently mathematicians believe that the Fibonacci ratio is used to make a composition the most aesthetically pleasing, but is this type of knowledge provable? There have been several artists in the past and present who use the Fibonacci ratio “from Leonardo da Vinci to Le Corbusier”  (McVeigh,”Why Golden Ratio Pleases the Eye: US Academic Says He Knows Art Secret.”), and surveys have shown that there is a favourable attitude towards it, but could this be random chance before we say with confidence that it is the cause of beauty? Since knowledge is in a constant state of flux, the more we know about this ratio, there is a greater chance that the knowledge on whether the ratio is the best fit for making a composition the most aesthetically pleasing might change, as a mathematician might find another formula. Also, people might prefer the fibonacci spiral due to personal opinion, past experiences, nostalgia and more, which leads them to like a composition more than another. We cannot know that the Fibonacci ratio is the best ratio to follow to make a composition the most aesthetically pleasing with complete knowledge. Goethe believed that “We know with confidence only when we know little; with knowledge doubt increases”. Discussing these aspects are relevant in both the natural science and mathematics world. By looking at the two areas of knowledge, we can see that what Goethe believed can be true to some extent, although there are some limitations. Goethe seems to be referring that people who are ignorant have a lot of confidence, but scientists are confident about the knowledge that they have because they acquire it mainly through sense perception which can be proven by reason. Mathematicians are also confident in their knowledge as they are able to prove theorems through axioms and deductive reasoning. Although, knowledge seems to be in a constant state of flux, meaning that we can never have certainty. And since we can never have certainty, doubt may increase.