Does Graphical evidence count as / contribute to a Proof in Mathematics? Several questions such as the following have an answer with pictures in it.

How find this inequality $\max{\left(\min{\left(|a-b|,|b-c|,|c-d|,|d-e|,|e-a|\right)}\right)}$
How prove this inequality $(a^2+bc^4)(b^2+ca^4)(c^2+ab^4) \leq 64$
How prove this inequality $\frac{2}{(a+b)(4-ab)}+\frac{2}{(b+c)(4-bc)}+\frac{2}{(a+c)(4-ac)}\ge 1$
How to prove this inequality(7)?

It's the bias of this author that these pictures are not merely an illustration,
but may be considered as an integral part of the proof. Yet I have the uneasy feeling that many "real" mathematicians do not wholeheartedly
agree with this. Which is the reason why this question is raised.
A possible counter argument could be that the picture is observed by our eyes and
that our eyes are not quite reliable in some sense. But mathematical formulas and text in a mathematical reasoning are observed by the same eyes, therefore the same counter argument would apply to a "common" formal proof. It's the same visual system that absorbs graphics, text and formulas. 
And ever since the ancient times, "algebra" (formulas) and "geometry" (pictures) have been
going hand in hand.When comparing geometry and algebra in this sense, 
courtroom-style ( > 60,000 lines ! ) algebraic proofs like those of the geometrically obvious Jordan Curve Theorem come into mind.

So, if graphical evidence doen't count as a proof, what is the real reason behind this?Weaker statement: can graphical evidence eventually contribute to a formal proof?
 A: Well, it certainly can work in an informal proof, since the purpose of an informal proof is rhetorical. Its purpose is to persuade a reader that there are good reasons to believe a formal proof exists, and to convey the intuition behind the proof strategy. But it's not part of a formal proof because a graph is not a formula in a formal language.
I don't care for pictures since A) the areas of my interest are non-numerical and don't lend themselves to graphing or visual depictions, and B) a few expressive formulae tell me volumes more than a picture.
As for the "but you need to use your eyes to read formulae too" argument, I think it's just plain silly. There's a world of difference in ease of mistaking, say, an 89 degree angle for a 90 degree angle, and in the ease  of mistaking $A\to B$ or $\mathcal{P}(x)$ for other typographical strings. There are loads of examples of deceptive diagrams, but I can't think of many examples of deceptive typography...
A: It depends on the goal of your proof: 


*

*if you just want to convince someone, then a graphical proof is a good option (well, to convince a non-scientific :-). 

*But if you want to construct a mathematical proof that can be verified and build upon, then you need to use a formal language. Formal means that it doesn't let place to interpretation: everything is defined. And I don't know of any formal graphical language. 


To be fully honest, their are always some assumption in a formal proof. Example: let "$n \in \mathbb{N}$" implicitly assume lots of definition on what is the set $\mathbb{N}$ and probably on operations (+ - $\times$) defined on it.
So this is not black or white. But graphical proof is either too far from being formal or, if it actually doesn't let place to interpretation, then most probably it is easy to prove using formal language. Example: 


*

*the graphical proof for the sum of odd numbers is very useful to get an intuitive understanding. But if a proper proof is needed, it is quite easy to deduce the equivalent (formal) recursive proof.   

*On the other hand, the missing square puzzle (tx to @SpamIAm for the link) shows how the lack of formal context can lead to a wrong conclusion. Here it is implied that the upper bound is the same at the start and the end (and so the area under it), which is actually wrong.

