I have attended some events devoted to “math appreciation”; those events tend to attract several people with different levels of knowledge of mathematics, and the topics covered tend to be broad enough to hopefully satisfy a large audience. I then suppose the purpose of those events is to help or encourage people to “appreciate” mathematics, as the name and the nature of the activities suggest, but I still wonder what “to appreciate mathematics” could mean. If one focuses on meaning of words, the Latin root of “to appreciate”, appretiare, and from it comes pretium, meaning price, seems to suggest that to appreciate something is to put some value on it, not necessarily pecuniary. However, I am not sure if this meaning of appreciation would necessarily involve emotional attachment to the subject, while the converse seems to be plausible. Hopefully, someone will help me clarify this matter.
If one accepts the etymologic interpretation, could it be that the level of appreciation for mathematics be the same from an expert and from a novice? I can imagine different possibilities: it seems obvious, or tempting, to suppose that an expert in a field must appreciate mathematics while this is not necessarily the case for a non-expert. A justification may be that a constant contact with the subject may lead one to enjoy it, and this enjoyment may increase over time, but someone who has only seen or learn some simple facts about math may not yet experience any attraction to the subject, which may depend on how an introduction has been done. Nevertheless, it may be that someone does advanced mathematics merely for another purpose while a novice chooses to study more mathematics just for the love of it. In such a case, who between the two is likely to appreciate math?
If those events succeed in their noble endeavor, what about mathematics training programs? Would making students appreciate mathematics be a goal of those programs? I have heard stories of people who happen to love mathematics after training in some schools; I then suppose this could be a possibility. I also have heard rather stark criticism of mathematics from people who seem to have had a bad experience during their training. Could it then be that those unfortunate students were expected to appreciate math before they decide to have further training in the subject?
What do you think?