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There is a concept called 'Infographics' that uses lots of colourful diagrams and graphs and artwork to visually depict some set of concepts and tries to explain the ideas through pictures. I recommend these Infographics to any person trying to learn some complicated principle in Math, say. I was wondering if there are any easy-to-comprehend infographics for hard subjects like Category theory or Topology?

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    $\begingroup$ People learn/understand differently. Some concepts are extremely hard to force into images. And doing so is moreover a very, very underdeveloped skill. $\endgroup$ – vonbrand Feb 18 '16 at 2:22
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For topology, Peter Saveliev has written:

Topology Illustrated.

A partial draft is available on the author's website, in case you would like a preview of some sections.

True to the title, it is heavily illustrated. While there is certainly plenty of explanatory text, the large number of pictures and diagrams could be seen as a form of infographics.

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For complex variables, there is the famous "visual" book

Tristan Needham, Visual Complex Analysis

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  • $\begingroup$ Tristan Needham's book is great, I have a copy. There is also one on 'Visual Group Theory' from the Math. Assoc. of America. I haven't found much else. The Infographics I mentioned would be a great 'medium' for Advanced Math. $\endgroup$ – 201044 Jan 16 '15 at 6:33
  • $\begingroup$ I think many hard concepts in math or science could be explained in a MUCH simpler fashion with clever art and diagrams. Even animated gif documents on a computer that show moving surfaces or graphs could help immensly. The Wolfram math site has what they call 'cdf' documents that stands for 'calculating' document format I think. Like a larger version of an animated gif document. The cdf has many changing demonstration abilities. So why is artistic presentations and mathematics usually separate in many math books?? $\endgroup$ – 201044 Jun 20 '15 at 5:13
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The slides of Dror Bar-Natan are excellent examples of such mathematical "infographics".

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In addition to Needham's famous book mentioned in Gerald Edgar's answer, there is

Visual Complex Functions: An Introduction with Phase Portraits by Elias Wegert.

The book is richly illustrated with colour diagrams of complex functions, especially the "phase portraits" mentioned in the title, as can be seen on the author's website for the book.

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Traditionally (say up to the last 40, 50 years?) images were extremely expensive to produce and distribute (line graphs had to be drafted by hand, other images had to be created by expensive methods, colour meant special pages in the book), and thus used sparingly. Creating, distributing and viewing videos was much worse. As a result, people streamlined methods to make their point without images. That is hard to unlearn.

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