Influential Visual Math Thinkers: Penrose, Mendelbrot, Arnold, Atiyah

In summary, there are several influential mathematicians who are known for their visual thinking and use of diagrams and drawings in their writings, such as Roger Penrose, Benoit Mandelbrot, Vladimir Arnold, Sir M. Atiyah, John Baez, and Tristan Needham. However, the question is not whether they are visual thinkers, but to what degree. Some notable names mentioned in this conversation are Milnor, Thurston, Hilbert, Felix Klein, and Cornelius Lanczos, who have varying levels of visual thinking in their work. It is also noted that being influential is not as important as being able to teach others.
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Do you know any influential mathematicians that are visual thinkers? especially those who wrote books.
For example mathematicians that think and write like Roger Penrose,Benoit Mendelbrot,Vladimir Arnold,Sir M.Atiyah who are very keen on using diagrams and drawings in their writings.
 
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The question is to what degree are they visual thinkers, rather than whether they are or are not. Do you really care if they are influential or just if they can teach you something? Personally, I could care less if they are influential. I only care if they can teach me something.

As far as influential...Milnor has said he is very visual, although I find some (not all) of his writing to be a bit on the formal side. Bill Thurston. Hilbert, to some degree. Felix Klein. Cornelius Lanczos. John Baez, to some extent.

Tristan Needham, although he seems to be mainly influential as the author of Visual Complex Analysis, which is a must read for any visually inclined math student.
 
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Related to Influential Visual Math Thinkers: Penrose, Mendelbrot, Arnold, Atiyah

1. Who are the influential visual math thinkers?

The influential visual math thinkers are Roger Penrose, Benoit Mandelbrot, Vladimir Arnold, and Michael Atiyah.

2. What contributions did Roger Penrose make to the field of math?

Roger Penrose is a mathematician and physicist who is best known for his work on the theory of relativity and black holes. He also made significant contributions to the mathematical fields of geometry and topology, including the development of Penrose tilings and the Penrose triangle.

3. How did Benoit Mandelbrot revolutionize the study of fractals?

Benoit Mandelbrot is known as the "father of fractal geometry" for his groundbreaking work on fractals, which are complex and infinitely repeating patterns found in nature. He developed the famous Mandelbrot set and helped to establish fractal geometry as a new branch of mathematics.

4. What is Vladimir Arnold known for in the world of math?

Vladimir Arnold was a renowned mathematician who made significant contributions to the fields of dynamical systems, differential equations, and singularity theory. He is also known for his work on the theory of bifurcations, which is the study of how systems change when a parameter is varied.

5. What are some of Michael Atiyah's notable achievements in mathematics?

Michael Atiyah was a mathematician who made groundbreaking contributions to various areas of mathematics, including topology, geometry, and algebraic geometry. He is best known for his work on K-theory and the Atiyah-Singer index theorem, which has applications in theoretical physics and differential geometry.

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