What attracted me so strongly and exclusively to mathematics, apart from the actual content, was particularly the specific nature of the mental processes by which mathematical concepts are handled. This way of deducing and discovering new truths from old ones, and the extraordinary clarity and self-evidence of the theorems, the ingeniousness of the ideas... had an irresistible fascination for me. Beginning from the individual theorems, I grew accustomed to delve more deeply into their relationships and to grasp whole theories as a single entity. That is how I conceived the idea of mathematical beauty...

From early youth I endeavored to read books in the right way and I was fortunate in having a good memory and intelligence to assist me.

I loved mathematics and science-related subjects.

The historical order is very interesting, but accidental and capricious; if we would to understand the growth of knowledge, we cannot be satisfied with accidents, we must explain how knowledge was gradually built up.

I could at times be overly emotional, but was lucky to have the kind of orderly mind that is good at categorizing things.

It is provable both that the historical sequence was, in its main outlines, a necessary one; and that the causes which determined it apply to the child as to the race. ...as the mind of humanity placed in the midst of phenomena and striving to comprehend them has, after endless comparisons, speculations, experiments, and theories, reached its present knowledge of each subject by a specific route; it may rationally be inferred that the relationship between mind and phenomena is such as to prevent this knowledge from being reached by any other route; and that as each child's mind stands in this same relationship to phenomena, they can be accessible to it only through the same route. Hence in deciding upon the right method of education, an inquiry into the method of civilization will help to guide us.

I came into history from a primary concern with mathematics and science. This has been a tremendous help to me as a person and as a historian, although it must be admitted it has served to make my historical interpretations less conventional than may be acceptable of many of my colleagues in the field.

I could at times be overly emotional, but was lucky to have the kind of orderly mind that is good at categorizing things

I'd never had a mind for math. ... It was a logic that made little sense to me. In my perception, the world wasn't a graph or a formula or an equation. It was a story.

On the one hand, all science, and indeed all thinking starts from and rests upon notions of order; what marks the Middle Ages is that their order was always a hierarchy. And on the other hand what marks the scientific view is not that it turned to the mechanism of causes, but that it saw the world as a mechanism at all—a machine of events.

It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me.

I have come to recognize that the reason I devote myself to research, and to the building of theory, is to satisfy a need for perceiving order and meaning, a subjective need which exists in me.

He seemed to thrive on creating a sense of order, on understanding the tasks to be taken care of.

I had been sitting in Joan Countryman’s living room for two hours talking about mathematics. My pulse was steady, the hand that held my note-taking pencil didn’t shake and wasn’t even clammy. Where was that old math anxiety? I hadn’t been at any loss for questions; they came to me naturally. Like the process of writing, the process of asking questions had been a form of learning, raising further questions and telling me what I wanted to know next. I was genuinely curious. It never occurred to me that this was a subject I wasn’t supposed to be any good at. What did occur to me was that mathematics was not some arcane system of numbers; it was a language, a way of putting thoughts together. I might never master the language — my checkbook might still go unbalanced — but at least I had begun to glimpse what the language was trying to say and how it could help people to understand the world around them.