Areas of maths thats hand wavy?

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SUMMARY

The discussion centers on the concept of "hand wavy" mathematics, emphasizing that many mathematical areas initially lack rigor but become established over time. Notable examples include Fourier series, which faced skepticism from mathematicians during their inception due to their informal presentation. Similarly, Euler's solution to the Basel problem involved a non-rigorous proof that was only formalized later. This highlights the natural progression of mathematical development from informal to rigorous.

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  • Understanding of basic mathematical concepts and terminology
  • Familiarity with Fourier series and their historical context
  • Knowledge of Euler's contributions to mathematics
  • Awareness of the evolution of mathematical rigor over time
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  • Research the historical development of Fourier series and their acceptance in mathematics
  • Study Euler's methods and proofs, particularly regarding the Basel problem
  • Explore the concept of mathematical rigor and its evolution in various fields
  • Investigate other mathematical concepts that started as informal or "hand wavy" and became rigorous
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Mathematicians, educators, students, and anyone interested in the historical development of mathematical concepts and the transition from informal to rigorous mathematics.

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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.
 
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.
 

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