...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.
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, … - Paul Halmos
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, …
- Paul Halmos
Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reas… - Paul Halmos
Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reas…
The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profo… - Paul Halmos
The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profo…
The library is the mathematician's laboratory. - Paul Halmos
The library is the mathematician's laboratory.
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 Halmos
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.
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method. - Paul Halmos
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.
A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant. - Paul Halmos
A smooth lecture... may be pleasant; a good teacher challenges, asks, irritates and maintains high standards - all that is generally not pleasant.
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mat… - Paul Halmos
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mat…
The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites. - Paul Halmos
The beginner should not be discouraged if he finds he does not have the prerequisites for reading the prerequisites.
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