Many a times, mathematics is believed to be a logical subject. However, without imagination, mathematics would not be born in the first place. Students are given definitions and formulas to better their understanding in mathematics. Do we question the credibility of these tools or is there more to it? I would claim that mathematics is innately perceptive, rather than logical.
An idea has to surface to allow a written infrastructure to be built on, hence enabling communication between the authors and readers. Mere written expressions do not mean anything without an idea bound to it.
Imagine an open space with cones placed adjacently on it, a skater can follow the cones, leading to a straight path. This is analogous to the coordinate system which opens up a wide spectrum of branches in mathematics. It would be impossible to conceive ideas without imagination. Zero, a number invented by the Indians, is a substitute to nothingness, a calling for readers to imagine that naught plays a factor to the expression of a number.
The vastness of imagination is boundless and complex. The quality of expression of any idea can be compromised with written expressions or depiction, simply because the transit between thoughts and words is limited to experience. As no one shares the same experience as the author, it will only be absolute that the reader cannot follow the author’s chain of thought exactly.
One of the greatest mathematicians of all time, Albert Einstein, produced a theory on relativity with sheer imaginative power. He then expressed his ideas through mathematics, which baffle readers throughout centuries. Imagination was further tapped to create the complex plane, an imaginative plane impossible to be expressed in real number. These are examples of perception over logic.
Logic, however, binds mathematics to reality so as to enable mathematics to be applied in real-life applications. This very fact allows formulas, definitions and rules-of-thumb to exist. Sir Isaac Newton could not have created the laws of motion. Dr John Nash, a Nobel laureate, could not have come up with game theory, which plays a large part in financial decisions presently. Mathematical rigour is significant in mathematical literature, and is the bedrock of all mathematical assumptions, as many people misunderstand the ramifications of mathematical rigour.
Logic and perception may not be mutually exclusive, for logic itself is a manifestation of perception. It is more important to see the whole picture (by being perceptive) than scrutinise on the details and see where the clues lead you (by being logical). Perception deserves a larger credit than that.