Is it appropriate to say that mathematical knowledge has intrinsic value for mathematicians?

Question

I have been toying with the idea of value for a while and came up with this question a few days ago.

I think that it is impossible to say that mathematical knowledge has intrinsic value for mathematicians for the following reason:

Although mathematicians working especially in inapplicable fields of mathematics say that they love number theory or set theory for the "sake of itself," the whole premise of this statement rests on the idea of mathematical beauty. The elegance of the equations and the identities is what affines them to work in this field. All this is good, but by the very act of attaching something to even the purer areas of mathematics, they in essence, value knowledge outside its realm or simply put they do not value the Fermat Little Theorem because it exists but because it is elegant and in doing so they have given it a further extension.

This is my argument. Please do point out any inconsistencies or generalizations and also I would love to read any counter-arguments.

Answer 1

I would be wary generalizing all of mathematicians, but you make a valid point. When a person uses an English phrase in the form of "I seek X for the sake of itself," that phrase is used to state that that person believes X has intrinsic value. Thus people who study math "for the sake of itself" self identify as people who believe math has intrinsic value.

Whether that extends to all mathematicians is a much more nuanced question. It seems entirely possible that an individual labeled as a mathematician could study math because it is a tool to achieve a goal. On the other hand, it is also possible to define "mathematician" to be "someone who believes math has intrinsic value" if you are comfortable with your definition potentially straying from the "mathematician" used by others who do not share your definition.

Answer 2

I think that a mathematician/scientist is nothing different from an explorator, I mean a person who is physically exploring a place. Why the explorator is exploring? The taste for exploration is actually a basic instinct of any animal, it is good, from an evolutionary point of view, to have this kind of taste because it results in collecting potentially useful information, useful for survival and reproduction. This is true for the dog exploring his neighbourhood but also for a man building a science. The taste for exploration is mixed and reinforced by different incentives, one is beauty as you mentioned, another is challange (this is probably mostly human): feeling challanged by a difficult task (reaching some high peak) and then having the reward of looking everything with your new superior point of view.

To answer your question I would say that the driving force of a mathematician is not "directly" the quest for knowledge, altought it is the result. Knowledge in itself wouldn't be pursued if one wouldn't have the taste for exploration or the urge to solve some kind of real problem.

On the other hand if a community of mathematicians/scientists would be required to express what is the valuable thing they are working on they wouldn't say that "the community" is working to create beauty and achieving specific results as a challange to themself.