Summary

Uses of mathematics

Mathematics isn’t only applied to the calculation of your GPA: it’s also applied to the arrangement of goods in supermarkets, barcodes, credit cards, fingerprinting, postal codes, and so on. But if you only focus on practical matters such as these, pure mathematics can’t develop, and when that happens, not only can’t we solve real-life problems such as those aforementioned, applied mathematics can’t develop either.

Abstractions

Symbols and formulas, which make mathematics look hard, are called abstractions. Notwithstanding whether you add an elephant to a group of two elephants, or add a cicada to a group of two cicadas, they can all be described as 2 + 1 = 3, which is, despite looking quite simple, nonethelessly an abstraction. If it wasn’t for abstraction, we would have needed to do separate calculations for adding elephants, cicadas, watermelons, and apples. But thanks to abstraction, we don’t have to do that.

Abstractions help to make problems more approchable. Let’s look at an example. This is a poem in Lilavati by Bhaskara, a mathematical treatise. I only had the Korean translation, so you’ll have to make do with my translation of the Korean translation.

---

O, beautiful lady!
Show me your wisdom, not unlike your fragrance.
In a garden of flowers do buzz bees;
One fifth flies to the magnolias,
one third flies to the morning glories,
and the difference of those two flies to the azaleas.
The one remaining hesitates between the fragrances of pandanuses and jasmines,
as if the solitude of a man trying to make two lovers talk,
buzzing about in the void.
Prithee tell me, how many bees are there flying about in the garden?

---

Let’s solve this using modern symbols. If we denote the number of bees as ‘x’, the equation would be:

x – x/5 – x/3 – 3( x/3 – x/5 ) = 1

. Multiplying 15, the least common multiple of 3 and 5, we can simplify this equation into this:

15x – 3x – 5x – 3( 5x – 3x ) = 15

, which is simplified to:

15x – 8x – 6x = 15

, which solves to x = 15, meaning there are 15 bees in the garden.

Here, you can see how you can make problems more approchable using mathematics. Most problems we encounter today are made approchable using mathematics.

Implication

Using abstraction, a type of mathematical thinking, you can solve complex real-life problems easily.

Underlying context – Background behind

There are people who hate symbols and functions in mathematics. Sometimes, people say ‘alphabets should stay in English class’ in Reddit.

Notions – Key ideas

Abstraction: reducing a complex concept into a less complex mathematical concept

Index – Source(s)

How to Think Like Mathematicians / 피타고라스 생각 수업
06 Categorizing Day-to-Day Life by Problems | Symbols and Classification / 일상을 문제별로 분류하는 법 – 기호와 분류

Trajectory – Where I’m headed now

Not applicable