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
...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.
Interpretation
What this quote means
Great mathematics often stems from specific examples, as they reveal the essence of broader concepts.
In this quote, Paul Halmos emphasizes the importance of concrete examples in understanding mathematical concepts. He suggests that many seemingly general principles in mathematics can ultimately be traced back to specific cases that enlighten and clarify the abstract ideas, thus underscoring the value of practical instances in the learning and application of mathematical theories.
Themes
MathematicsExamplesEducationConcreteConcepts
In practice
Example use cases
This quote can be used in a classroom to encourage students to look for specific examples when learning new mathematical concepts.
More from Paul Halmos
All quotes β[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.
Paul HalmosRead
Similar quotes
I use the verb 'to torment,' as I observed to be your own method, instead of 'to instruct,' supposing them to be now admitted as synonymous.
Jane AustenRead
Reading is at the center of our lives. The library is our brain. Without the library, you have no civilization.
Ray BradburyRead
Teachers need to be comfortable talking about feelings. This is part of teaching emotional literacy - a set of skills we can all develop, including the ability to read, understand, and respond appropriately to one's own emotions and the emotions of others.
Daniel GolemanRead
Don't dumb down; always write for your top five percent of readers.
Martin AmisRead
Unless the schools provide our children with a vision of human possibility that enlightens and empowers them with knowledge and taste, they will simply play their role in someone else's marketing schemes. Unless they understand deeply the sources of our democracy, they will take it for granted and fail to exercise their rights and responsibilities.
Diane RavitchRead
There are many little ways to enlarge your child's world. Love of books is the best of all.
Jackie KennedyRead