3. Is it better to “have questions that can’t be answered than answers that can’t be questioned” (adapted from Richard Feynman)? Discuss with reference to mathematics and one other area of knowledge.

The “Is it better to…” part of November prescribed title #3 should not be overlooked.  If you choose this prescribed title your thesis must directly answer the question.

The phrase “questions that can’t be answered” is the first key phrase in November prescribed title #3 that needs to be addressed.  First of all, there is some debate as to whether some questions have been answered or not.  One researcher may consider a question answered but other another researcher may disagree.

Also, consider why some kinds of questions cannot be answered.  In history, for example, some questions cannot be answered because of a lack of definitive sources.  Ambiguity in language in a document may mean the source could be interpreted in different ways which makes is difficult to answer particular questions.  In the arts, some questions cannot be answered definitively because of the interpretive nature of art. Or perhaps a particular piece of art is so closely connected to a specific culture / society that it cannot be used to answer some questions.

In other cases there are theoretical questions that cannot be practically researched and therefore the questions cannot be answered definitively.  Also, some research which could provide answers to some questions cannot be conducted for ethical reasons.  Some medical / psychological / social experiments that were done in the past that may have provided information are not longer able to be conducted.

There are a number different possible approaches to the phrase “answers that can’t be questioned.”  One obvious one is religion, where in some questions there are believed to be absolute answers than cannot be questioned.  However, this is not true in all aspects of all religions – questioning is a significant part of many religious beliefs.

Some specific examples show that there are answers for a particular situation but the underlying mechanism isn’t understood well enough to be able to question it.

In other cases, there are answer that cannot be questioned because the person or group that has provided the answers has some sort of authority.  That authority may or may not prove beneficial to producing some kinds of knowledge.  A dictator, for example, may be able to use fear to gain information about political rivals but that style of leadership obviously has significant blindspots.  Dictators are not known for valuing knowledge that contradicts his / his beliefs.

In rare cases (e.g. there are some in mathematics) a question has been answered so irrefutably that there seems to be no point in questioning the answer.