I am trying to respond to a question "Why is mathematics so difficult?" asked by willian.sizzla on Community Chat:
Mathematics is probably not difficult the way people think, but our mentality makes it look that way. It is something that has to do with the earlier mental and psychological experiences passed from generation to generation.
But, here I will argue, in the line as to why mathematics is difficult.
Many people find mathematics learning difficult because they are unable to relate a hierarchy of interrelated concepts and ideas. However, its practical implication and association to our daily life does neither come readily into our mind nor can it be easily imagined for most branches of mathematics, since they seem to be more abstract to be comprehended by many. This does not mean mathematics has little or no applications, it is that we are not able to figure out how to meaningfully and practically connect its teaching and learning to our daily life. Things become more difficult due to mathematics objectivity, as most mathematics problem need one to arrive to a particular answer with proper and mathematically validated proofs, reasoning and logic - no room for opinions, suggestions or fambling. Most people will have hard times learning mathematics if they don't have basics in mathematics, because in most cases, if not all, mathematics is ordered hierarchically, from basic to advanced levels, at the same time concepts and ideas are strongly interdependent. As one advances in Mathematics learning, he/she will notice a strong coupling between various branches of mathematics! You will need one branch or several to learn another. Very often, one needs a lot of thinking, reasoning and argumentation to arrive to a sound and acceptable conclusion for a problem that seems obvious!
For example, in regard to your question, a typical mathematician would not readily start to respond to your question, instead would start by asking you questions such as,
what do you mean by difficult? Can you prove your claim that mathematics is difficult? How do you know mathematics is difficult, and so on!
In mathematics, no statement or claim can be accepted without proof, unless it is impossible to deny or disprove!
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Why is mathematics so difficult?
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