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Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.
--
As quoted in Stephen Hawking: A Biography (2005) by Kristine Larsen, p. 43

 

Stephen Hawking

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Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i.e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.

 

Hans Reichenbach

 

Sometimes when I'm having a boring interview on the telephone, and I'm trying to think about something else because the questions are too boring, and I start looking around the room where I work, you know, full of books piled up to the sky, all different kinds of topics. I start calculating how many centuries would I have to live reading twenty-four hours a day every day of the week to make a dent in what I'd like to learn about things, it's pretty depressing.[...] You know, we have little bits of understanding, glimpses, a little bit of light here and there, but there's a tremendous amount of darkness, which is a challenge. I think life would be pretty boring if we understood everything. It's better if we don't understand anything... and know that we don't, that's the important part.

 

Noam Chomsky

 

That night Paradine slept badly. Holloway's parallel had been ill-chosen. It led to disturbing theories. The x factor — The children were using the equivalent of algebraic reasoning, while adults used geometry.
Fair enough. Only —
Algebra can give you answers that geometry cannot, since there are certain terms and symbols which cannot be expressed geometrically. Suppose x logic showed conclusions inconceivable to an adult mind?

 

Lewis Padgett

 

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

 

Benoit Mandelbrot

 

Since whatever we do has to be part of a team, part of a community, we have to attempt to bring together those who have the same conviction, see the same things. Then it becomes a matter of time, when one or the other will prevail. Fortunately, there is all this diversity, and if not for that, problems would not be solved.

 

Jonas Salk