A saying of David Hilbert

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Quoting tim wood

"A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street."

And that is the explanation for "what is clear and easily comprehended attracts".

Quoting A Realist

Are you sure David?
I would think that what is "clear and easily comprehended" is uninteresting and boring,

What you would think is wrong: Fermat's Last Theorem

However, the world of mathematics is so immense and in part has become so abstract that one mathematician might not be able to convey to another mathematician a recent result without some difficulty.

The perfect math problem is complicated enough to challenge us, but easy enough so we can find its solution. The reward is an inner satisfaction. Nobody can give you inner satisfaction but yourself.(*)

(*) Theists are, as usual, exempt from believing this maxim.

Quoting tim wood

A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.

With a little luck, the first man (or woman) on the street you meet is a seven-times Field Prize award winner.

Quoting A Realist

Are you sure David?

What was the context? Context may help us know what he meant.

My favorite Hilbert quote is when he spoke before the faculty senate of Göttingen, arguing that his brilliant student Emmy Noether deserved to be given a position as Privatdozent. Those opposing her said that young German men returning home from the war (WWI) would not be willing to be taught by a woman. Hilbert famously said, "We are a university, not a bathhouse!" But she was denied an academic appointment on account of her sex.

Reply to fishfry I am not sure that a university is not a bathhouse...
Anyway the context is the excerpt of tim wood's first post.
Obviously every x is different from y, but x has properties or qualities similar to y.
:-)
Anyway if something is too easy you lose interest in it, this is why life is so hard.
This is the case also in mathematics, if a problem you pose is too easy people won't be interested of course there's the saying of Feynman:
" According to the Nobel Prize-winning physicist Richard Feynman (Feynman 1997), mathematicians designate any theorem as "trivial" once a proof has been obtained--no matter how difficult the theorem was to prove in the first place. There are therefore exactly two types of true mathematical propositions: trivial ones, and those which have not yet been proven."

https://mathworld.wolfram.com/Trivial.html
So perhaps all of math is uninteresting and boring, though I would like to think that the fact that there are difficult proofs is to the contrary to Feynman's anecdotal quote.

Reply to A Realist This reminds me of my thoughts on beauty qua elegance, which is to say, the intersection of a phenomenon being interestingly complex, but also comprehensibly simple. Complexity draws one's attention into the phenomenon, seeking to understand it; and if that complexity is found to emerge from an underlying simplicity, beauty can be experienced in the successful comprehension of that complexity by way of the underlying simplicity.

That is to say, symmetries and other patterns, that allow us to reduce a complex phenomenon to many instances and variations of simpler phenomena, are inherently beautiful in an abstract way. This is the kind of beauty to be found in abstract, non-representational art, and also in places besides art such as in mathematical structures.

The tension here between interesting complexity and comprehensible simplicity is, I think, what underlies the distinction many artists, audiences, and philosophers have made between what they call "high art" and "low art".

- Those who prefer so-called "high art" are those with enough experience with the kinds of patterns used in their preferred media that they are able to comprehend more complex phenomena than those less experienced, but simultaneously find simpler phenomena correspondingly uninteresting.

- Those who prefer so-called "low art" (so called by the "high art" aficionados, not by themselves) instead find more complex phenomena incomprehensible, but are simultaneously more capable of taking interest in simpler phenomena.

Unlike the attitudes evinced in the traditional naming of these categories, I do not think that "high art", a taste for complex phenomena, is in any way inherently better than "low art", a taste for simple phenomena. In each case, the aficionados of one are capable of appreciating something that the other group cannot, while incapable of appreciating something that the other group can.

In my opinion, if any manner of taste was truly to be called universally superior, it would be a broader taste, capable of comprehending complex phenomena and so appreciating "high art", while still remaining capable of finding simple phenomena interesting and so appreciating "low art". In that way, audiences with such taste would be best capable of deriving the most enjoyment from the widest assortment of phenomena, both natural and artistic.

Quoting A Realist

According to the Nobel Prize-winning physicist Richard Feynman (Feynman 1997), mathematicians designate any theorem as "trivial" once a proof has been obtained--no matter how difficult the theorem was to prove in the first place. There are therefore exactly two types of true mathematical propositions: trivial ones, and those which have not yet been proven

This is nonsense and probably Feynman at his best at satire. :cool:

Reply to Pfhorrest You can make the claim that the complicated and complex is made of easy and simple to comprehend ideas which as a whole make the complex and complicated easy to comprehend.

In that case it's like a point in geometry which is zero dimensional but the the whole line which is made of infinite number of these points is one dimensional...

I feel like I have already discussed this before... :-) Dejavu.