Areas of maths thats hand wavy?

In summary, It is common for new areas of math to start off being "hand wavy" and only later become more rigorous through further study and development. This is not limited to specific areas, but rather a natural progression in the development of mathematics. Examples such as Fourier series and Euler's solution of the Basel problem demonstrate this pattern of starting with hand waving and then becoming more precise over time.
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Any areas in maths that's hand wavy? Is so where?
 
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Any area of math must be firmly grounded in order to be an area of math.

On the other hand, a "popularized" account of any area of math will probably need to be "hand wavy" not to be intelligible to the general public. It is not a matter of the "area" but of the depth to which an individual wants to study the area.
 
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Many important areas of math begin handwavy and are only later made rigorous. For example, Fourier series were scoffed by mainstream mathematicians when Fourier first thought of them because he handwaved a few things.

Euler's big breakthrough at age 29 was the solution of the Basel problem... except his "proof" by "factoring" sin(x)/x wasnt made rigorous until much later!

This is the natural way new areas of math are developed.
 

FAQ: Areas of maths thats hand wavy?

What are some examples of areas of math that are considered "hand wavy"?

Areas of math that are often considered hand wavy include topology, abstract algebra, and number theory. These fields often involve concepts that are difficult to visualize or explain in simple terms.

Why are these areas of math considered "hand wavy"?

These areas of math are considered hand wavy because they often involve abstract concepts and use non-intuitive notation and language. This can make it difficult for non-experts to understand and explain these concepts.

Are there any benefits to studying "hand wavy" areas of math?

Yes, there are many benefits to studying these areas of math. They often lead to groundbreaking discoveries and innovations in other fields such as physics, computer science, and engineering. Additionally, they can improve critical thinking skills and problem-solving abilities.

How can one better understand "hand wavy" areas of math?

To better understand these areas of math, it is important to have a strong foundation in basic math concepts and to practice visualizing and manipulating abstract concepts. It can also be helpful to seek out resources, such as textbooks or online lectures, that break down these concepts in a more approachable way.

What career opportunities are available in "hand wavy" areas of math?

There are many career opportunities available in these areas of math, including research and academia, data analysis, cryptography, and computer science. These fields require strong analytical and problem-solving skills, making them well-suited for individuals with a background in "hand wavy" math.

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