Why real mathematicians don’t use numbers?

Posted by Andrew Smith

There is this joke about how real mathematicians don’t use numbers. It seems funny but most of the time it is true. When I was studying Mathematics during my school days, I felt that Mathematics is all about numbers – even numbers, odd numbers, prime number, real numbers, whole numbers, imaginary numbers and the list goes on. As I moved up the education ladder, slowly I was exposed to various symbols which helped me simplify the Math problems or should I say that the symbols helped my professors complicate the math assignments and examinations questions.

Apart from numbers, we have mathematics operators (∏, ∑, √ , ∞, ∫, ≠, <, > ), Alphabets (x, y, z, a, b.....), Greek symbols (λ, β, δ, ε, Π, Ψ, Δ, ξ) etc. which are used in various math topics. We also have trigonometric functions (  ), Limits, logarithms, calculus. These symbols open a door to various mathematical mysteries which even a Math Post-graduate might not be aware of.

The symbols used in mathematics are quite unique to its field and are deeply rooted in history. It all began when people started using arithmetic symbols to keep track of animals or bundles of food. Addition symbol was first used in the 1360s, followed by subtraction symbol in the 1480s. A French named Nicole Oresme used the + symbol to abbreviate “and”. The “+” and “-“symbols both were printed by Johannes Widmann in 1489. As more and more symbols were getting introduced in the 1500s and 1600s it became difficult to understand the mathematical meanings and ideas related to the equations in which symbols were used.

After reading the history of mathematics, I can say that a symbol is a non-word and non-number which represents a mathematical idea. When I started my first Math course in graduate, my mind was exploding with the amount of new symbols and mathematical notations. I was horrified thinking that I might never be able to understand these notations. I began by understanding the basic Math symbols and how they can be used in various mathematical notations. After practicing for more than 6 months, I developed by own style of writing symbols. Based on the various students I have studies with, I can say that everybody has their own style of writing these symbols. You can refer to the Old Pappus’ Book of Mathematical Calligraphy to perfect your style of writing math symbols.

So, the reason that mathematicians use more symbols is that the deeper you go into the subject, the easier it is to simplify it using symbols. Symbols can convey a large amount of information in a simplistic manner. The real beauty of mathematics lies in the mathematical notation and hence mathematicians tend to use symbols in their solutions and analysis.