What Are the Jewels in the Crown of Mathematics? Is There a Picture of Them?

[Jim Kata]

I've read many places where a statement like number is the crown jewel in the crown of mathematics, or complex analysis is a jewel in the crown of mathematics. My question, is it defined what exactly are the jewels in the crown of mathematics, and has there been a picture drawn of it?

 

[HallsofIvy]

The answer is "no".

 

[Deveno]

it's just a metaphor. just as diamonds are admired for their brilliance and clarity, in the same way certain fields of math are admired for their purity and elegance. this is almost always a matter of subjective taste, there is no actual "crown".

both the natural numbers, and the complex numbers are held to have a certain sort of sublime beauty to them, and this beauty is partly because they can be completely characterized in terms of their properties. in lay terms, we have shifted the question from: "what is a number" to: "what can a number DO".

just as "2" represents a level of abstraction having nothing to do what "whatever-it-is you are counting two OF", in the same way the natural numbers and the complex numbers represent certain "smallest" things that have "pleasing" properties.

other such "smallest" things occur elsewhere in mathematics, the real numbers being one such example, the rational numbers being another. one particularly important, but humble example is a set containing just one element, often written {*}, or sometimes simply as 1, a concept the ancients called "unity", and regarded as "indivisible".

even though for many people on earth, the days of royalty being an example of what was finest in human culture are long gone, the metaphors persist in our language, such as budweiser being called the "king of beers", although one hardly expects to see some amber bottle ensconced on a throne somewhere.

 

[tiny-tim]

Hi Jim!

… has there been a picture drawn of it?

Hey fellas!

Just because it doesn't exist, that doesn't mean nobody's ever drawn a picture of it …

in fact, I'd be surprised if there isn't one! ​

Sooo … does anyone know of such a picture?

(a google image search doesn't show anything )

 

[CellCoree]

I would like to clarify that the phrase "jewels in the crown of mathematics" is not a scientifically defined concept. It is a metaphor that is often used to describe certain branches or areas of mathematics that are considered particularly important or valuable.

Some common examples of these "jewels" include number theory, which deals with the properties of numbers and their relationships, and complex analysis, which studies functions of complex numbers. However, this list is not exhaustive and different mathematicians may have different opinions on what they consider to be the jewels in the crown of mathematics.

To answer the second part of the question, there is no specific picture or visual representation of these jewels. Mathematics is a highly abstract field and its concepts are often difficult to depict visually. However, there are many diagrams and illustrations that mathematicians use to explain and visualize mathematical concepts, such as graphs, equations, and geometric shapes.

In conclusion, while the phrase "jewels in the crown of mathematics" is a common and poetic way to describe important areas of mathematics, it is not a scientifically defined concept and there is no specific visual representation of it. The true beauty and value of mathematics lies in its abstract nature and its ability to explain and describe the world around us.