``... let me plead ... for the highest consideration to be given to the pursuit of pure knowledge as well as technical training, not neglecting mathematics, once called the Queen of the Sciences. The wind bloweth where it listeth, and the spirit of knowledge does not follow the quest for wealth and power; but the creation of new knowledge makes for the high repute of a nation, alike in the days when its influence is dominant and more in the distant days when its doings shall have been recorded on the scroll of time.''

__A. R. Forsyth, Mathematics in life and thought, Gateway to the Great Books - Mathematics

"Math teachers (just like other teachers and professors) require students to memorize information: formulas, definitions, theorems, proofs, and so on. The common response by students is that this is a waste of time because they can look up these things. Well, they certainly can. That isn't the point I am debating. The problem is that you look up things that you know you don't know - and on top of that, you need to know fairly specifically what you don't know. This is where the problem comes - you have got to know the subject well enough that you know when you might use the item that you could look up. Without that knowledge, you won't know that there is a formula, proof, strategy, result, analysis, and so on, that can help.

"This quickly leads to a great fallacy in knowledge: You don't need to learn things that you can look up. But now we can look up about anything online or in a research library like the ones on many college campuses. This leads to the quick conclusion that you don't have to learn anything. What, then, becomes of the knowledge that forms our everyday thoughts? We can think only with ideas that are already formed in our minds. That is how we make sense of what we have experienced. With those ideas only in books, websites, videos, and so on, they are not available for us to think with - not until we have digested them and made them a part of us.

...

"Our thoughts come from what we know - not what we could know. We make sense of the world with the knowledge and beliefs in our mind, not with what we can look up on a smartphone."

__Douglas Corey, Brigham Young University, from maa.org/mathhorizons/supplemental.htm