“The reasons why I do things are difficult for me to understand and difficult for me to explain.”

On an article by Qunta magazine(when asked: Is there one big question that has always guided you?) https://www.quantamagazine.org/michael-atiyahs-mathematical-dreams-20160303
Context: I always want to try to understand why things work. I’m not interested in getting a formula without knowing what it means. I always try to dig behind the scenes, so if I have a formula, I understand why it’s there. And understanding is a very difficult notion. People think mathematics begins when you write down a theorem followed by a proof. That’s not the beginning, that’s the end. For me the creative place in mathematics comes before you start to put things down on paper, before you try to write a formula. You picture various things, you turn them over in your mind. You’re trying to create, just as a musician is trying to create music, or a poet. There are no rules laid down. You have to do it your own way. But at the end, just as a composer has to put it down on paper, you have to write things down. But the most important stage is understanding. A proof by itself doesn’t give you understanding. You can have a long proof and no idea at the end of why it works. But to understand why it works, you have to have a kind of gut reaction to the thing. You’ve got to feel it.

Part I: You Don't Have To Do A Thing
The Courage to Stand Alone (2001)
Context: Whatever pursuit you are indulging in, somewhere along the line it has to dawn on you that it is not leading you anywhere. As long as you want something, you will do that. That want has to be very, very clear. What do you want? All the time I ask you the question, "What do you want?" You say, "I want to be at peace with myself." That is an impossible goal for you because everything you are doing to be at peace with yourself is what is destroying the peace that is already there. You have set in motion the movement of thought which is destroying the peace that is there, you see. It is very difficult to understand that all that you are doing is the impediment, is the one thing that is disturbing the harmony, the peace that is already there.

Source: A Room with a View (1908), Ch.1

Source: Blindness (1995), p. 284

New York Times interview (1985)
Context: I think comedy is the most difficult thing in the world, I really do. One can always lament, you know — but to laugh in the face of life, that's very hard. And for me the great tragedian should also be a great comedian.

Preface
The Substitution of Similars, The True Principles of Reasoning (1869)

American Diplomacy (1951), World War I
Context: There are certain sad appreciations we have to come to about human nature on the basis of these recent wars. One of them is that suffering does not always make men better. Another is that people are not always more reasonable than governments; that public opinion, or what passes for public opinion, is not invariably a moderating force in the jungle of politics. It may be true, and I suspect it is, that the mass of people everywhere are normally peace-loving and would accept many restraints and sacrifices in preference to the monstrous calamities of war. But I also suspect that what purports to be public opinion in most countries that consider themselves to have popular government is often not really the consensus of the feelings of the mass of the people at all, but rather the expression of the interests of special highly vocal minorities — politicians, commentators, and publicity-seekers of all sorts: people who live by their ability to draw attention to themselves and die, like fish out of water, if they are compelled to remain silent. These people take refuge in the pat and chauvinistic slogans because they are incapable of understanding any others, because these slogans are safer from the standpoint of short-term gain, because the truth is sometimes a poor competitor in the market place of ideas — complicated, unsatisfying, full of dilemma, always vulnerable to misinterpretation and abuse. The counsels of impatience and hatred can always be supported by the crudest and cheapest symbols; for the counsels of moderation, the reasons are often intricate, rather than emotional, and difficult to explain. And so the chauvinists of all times and places go their appointed way: plucking the easy fruits, reaping the little triumphs of the day at the expense of someone else tomorrow, deluging in noise and filth anyone who gets in their way, dancing their reckless dance on the prospects for human progress, drawing the shadow of a great doubt over the validity of democratic institutions. And until people learn to spot the fanning of mass emotions and the sowing of bitterness, suspicion, and intolerance as crimes in themselves — as perhaps the greatest disservice that can be done to the cause of popular government — this sort of thing will continue to occur.