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Mathematics is a Privilege

In the olden days, education was a privilege in which many times only the wealthy could

afford to attain. Now, many students do not realize how fortunate they are to have been given the

opportunity for a free education in which we are able to learn mathematics, and many other

subjects for free. They just go to school because it is the norm, and they never learn to appreciate

the knowledge being passed down to them from the greatest minds of all time. Often times

students initially learn mathematics by being taught how to add, subtract, multiply, and divide,

i.e., the fundamentals. When it is time to go on to more complicated calculations, letters or

symbols are introduced, and that is when many students begin to think the new verbiage is

complicated, or even think they are incapable of understanding higher levels of mathematics. In

reality, the use of symbols and letters greatly simplify calculations. We owe this gift to a great

many mathematicians throughout history, because without the new symbols, mathematics would

be a whole lot more complicated and confusing.

Imagine having to read an entire mathematical

textbook or manuscript in Latin, before the introduction of

symbols. One would probably be confused in the first

paragraph when having to decipher what is being added or

subtracted to what. Imagine, then, having to explain square

roots, division, infinite sequence, all without symbols. I feel

lightheaded just thinking about it. The picture at the right is

an example from Dr. Shanyu’s History of Mathematics

textbook of a Latin mathematics book without notation. Very complicated, to say the least!

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There have possibly been countless mathematicians who attempted to use abbreviations

or symbols in mathematics, and one of those first attempts was the use of the word “et,” which

means “and.” A man named Nicole d' Oresme, who lived during the time period of 1323-1382,

“may have used a figure which looks like a plus symbol as an abbreviation for the Latin et…in

Algorismus proportionum, believed to have been written between 1356 and 1361” (Miller).

Germany is often credited with actually having been the country to introduce the use of the + and

– symbols, but it was Francois Viète who popularized their use. Francois Viète was a French

mathematician born in Fontenay-le-Comte, and he used the modern algebraic notation in his

book artem analyticam isagoge, which was published in 1591. Though he mainly practiced law

throughout his adulthood, in his leisure time, he practiced mathematics and popularized the use

of many symbols we use today.

Viète was also one of the first mathematicians to replace numbers by letters, thus

improving the theory of equations, and subsequently, was “the first mathematician to have an

impact on the development of the algebraic notation in the history of mathematics” (Ji). Letters

were utilized as symbols for quantities, where vowels and constants were used for unknown, and

known quantities, respectively. Later, René Descartes, a French mathematician, would further

formalize the use of letters by making it a convention to use letters at the beginning of the

alphabet for known quantities and letters at the end of the alphabet for unknown quantities.

Viète also used the fraction bar, and began the process of using symbols for

multiplication and taking the square of a number. For example, he used the word “in” when he

wanted to multiply and “quadratum” when he wanted to take the square of a number. So, to

multiply A and B, he would write A inB, and when he wanted a square of a number, say C, it

would be written as C quadratum. In today’s notation that is 𝐴  𝑥  𝐵 and 𝐶&, respectively. Because

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of all these great contributions, Viète became known as “the father of modern algebraic

notation,” rightfully so. Though he might not have contributed many complicated concepts or

proofs, the use of these symbols has greatly impacted mathematical computation and

understanding. His greatest contribution was the improvement in notation and though seemingly

trivial, this contribution was exceptionally helpful in the world of mathematics, the building

block of understanding the sciences and the world around us.

One of the most famous mathematicians that we do owe a great number of concepts to is

Leonhard Euler, a Swiss mathematician who lived from 1707 to 1783. Interestingly, Euler was

actually not able to learn mathematics through his school because it was so poor. Instead, his

father, Paul Euler, taught him some elementary mathematics, and from there Euler blossomed

into the genius he grew to be. He was so brilliant that he “once did a calculation in his head to

settle an argument between students whose computations differed in the fiftieth decimal place”

(Ji). His memory was absolutely amazing, which is probably what aided him in making the

contributions that he did. For instance, he introduced the summation symbol, Σ, and the symbol

𝑖  to denote the imaginary number −1. He also “used 𝜋 to denote the ratio of a circle’s

circumference to its diameter” (Ji). A fun fact about Euler is that in“1988, readers of the

Mathematical Intelligence voted [the Euler’s identity] “the Most Beautiful Mathematical

Formula Ever” (Ji). The identity is denoted by 𝑒,- + 1 = 0, and the reason it was voted so is

because it made use of the “notions of addition, multiplication, exponentiation, 0, 1, e, i, 𝜋, sine,

and cosine” in such a seemingly simple equation (Ji).

What’s even more fascinating about Euler is that many of his contributions were

published after he went completely blind in 1766. He was able to publish his books by dictating

them, published over 800 papers throughout his lifetime, and won 12 Paris Academy prizes. The

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Paris Academy held contests for mathematicians to solve problems that have never been solved

before. Some of the “challenges put forth each year typically involved current open problems,

including aberrations in the motions of Jupiter and Saturn, construction of winches, and the

application of hydrodynamics to seafaring” (Klyve and Stemkoski). Euler made about 15

submissions, so to have 12 prizes is truly remarkable.

These symbols are only a few of many that have been gifted to the world of mathematics.

Without these, mathematics would be a lot more tedious and confusing. The use of symbols

makes the dissemination of knowledge a lot easier and faster. Even someone such as Viète, who

was generally not considered a great mathematician, was able to contribute something so

wonderful and useful to mathematics. So, we need to remember no small contribution is too

little, and no excuse, such as being poor or even blind, is so small or large that it would hinder

our ability to change the world. Many mathematicians have proven throughout history that

adversity is not an obstacle. All we really need is the will to try.

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Works Cited

Ji, Sahnyu. "Lecture 23." History of Mathematics. n.d.

Ji, Shanyu. "Lecture 24." History of Mathematics. n.d.

Ji, Shanyu. "Lecture 30." History of Mathematics. n.d.

Klyve, Dominic and Lee Stemkoski. "The Paris Academy." n.d. The Eueler Archive. 9

November 2017. .

Miller, Jeff. "Earliest Uses of Various Mathematical Symbols." 2 June 2017. Jeff Miller Web

Pages. 6 November 2017. .