...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.
Paul HalmosRead
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.
Interpretation
What this quote means
Mathematics is a unified field representing truth, beauty, and interconnection in knowledge.
In this quote, Paul Halmos emphasizes that mathematics is not just a collection of separate disciplines, but rather a cohesive and interconnected body of knowledge. He views mathematics as embodying essential qualities such as security, certainty, and beauty, highlighting the intrinsic relationships among its various branches, suggesting that the essence of mathematics lies in its ability to reveal profound truths about the world.
Themes
MathematicsTruthBeautyKnowledgeInterconnection
In practice
Example use cases
During a seminar on the beauty of mathematics, this quote can be shared to inspire appreciation for mathematical concepts.
More from Paul Halmos
All quotes →It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.
Paul HalmosRead
Similar quotes
(On the energy radiated by the Sun) It's four hundred million million million million watts. That is a million times the power consumption of the United States every year, radiated in one second, and we worked that out by using some water, a thermometer, a tin, and an umbrella. And that's why I love physics.
Brian CoxRead
Freedom is the oxygen without which science cannot breathe.
David SarnoffRead
It is certainly true in the United States that there is an uneasiness about certain aspects of science, particularly evolution, because it conflicts, in some people's minds, with their sense of how we all came to be. But you know, if you are a believer in God, it's hard to imagine that God would somehow put this incontrovertible evidence in front of us about our relationship to other living organisms and expect us to disbelieve it. I mean, that doesn't make sense at all.
Francis CollinsRead
Equipped with our five senses - along with telescopes and microscopes and mass spectrometers and seismographs and magnetometers and particle accelerators and detectors sensitive to the entire electromagnetic spectrum - we explore the universe around us and call the adventure science.
Edwin Powell HubbleRead
Everyone in the astronaut program has a degree in a science field. The crew are the ones who do the experiments, help to design some of the experiments that come from other primary researchers. So it becomes very important that you have a science background.
Mae JemisonRead
We live in a society exquisitely dependent on science and technology, in which hardly anyone knows anything about science and technology.
Carl SaganRead