It is important to play e4 or d4 to 'control the center'. Myth or reality? Well, there are two premises in the question itself: 1) That e4 or d4 'controls the center'. 2) That 'Controlling the center'is something important. It appears to me that 'controlling the center' is the least of the benefits of a move  like e4 or d4. The fact is that it becomes mandatory to play e4 or d4 if you want to develop both bishops along their long diagonals(c1-h6 diagonal or a6-f1 diagonal). This seems to be the most important benefit of e4/d4 IMO and not 'controlling the center'. So while it may turn out that 1) e4 and 1) d4 give rise to good games for white I feel it may be more due to the rapid development which these moves allow rather than because these pawns 'control the center'. Indeed, sometimes, these pawns can be an obstacle for white's own pieces.(I am looking at things from white's perspective but the same argument can be similarly posed from the black player's perspective as well.). Do post your thoughts on this.
Let me start from top to bottom:


  It is important to play e4 or d4 to 'control the center'. Myth or reality?


Myth. 


  Well, there are two premises in the question itself: 1) That e4 or d4 'controls the center'.


When you play 1.e4/d4 you do not control the center, you physically occupy it.

To control the center, you will need more than a single pawn move-you need certain amount of developed pieces coordinated to control certain central squares.

1.e4/d4 simply fights for the center, you can not control it with just one pawn move-wish if it was that easy :)

Most importantly-you can not control anything unless your opponent allows you to-you can only fight for it.


  Well, there are two premises in the question itself: ... 2) That 'Controlling the center'is something important.


It is of utmost importance in the opening, as it allows you to completely control the game development. Controlling the center allows you to orient your actions towards the wings without worrying that your opponent can counter-strike in the center-thus usually refuting your plan or at least getting the equal play.

Also, you can open or close the game when you seem fit which usually can decide the game to your favor-not to mention the speed which your pieces get when centralized, since they can reach any part of the board in relatively equal amount of moves, contrary to the pieces posted at the wing.If we have a knight on d4, he can reach both wings at relatively equal amount of moves, but if it is posted on h3 then he needs a lot of moves to reach queen side which sometimes proves fatal.

Also, controlling the center hinders the activity and coordination of the opponents pieces-which enables you to start preparing for an attack or at least to create some serious weaknesses in their position.

In short-controlling the center is of paramount importance from the start to the end of the game-just remember that controlling is not the same as occupying the center.

To be honest, I haven't seen the opening that controls the center-all the modern openings either:


Fight for it. 
Divide the control-E.G. White controls d5 and e4 and Black controls d4 and e5, usually by blocking the center, or by exchanging central pawns.
One side "surrenders the center" giving the opponent space advantage, but in return gets huge pressure against that center from the sides or from the distance ( usually light pieces perform the pressure ).



  It appears to me that 'controlling the center' is the least of the benefits of a move like e4 or d4. The fact is that it becomes mandatory to play e4 or d4 if you want to develop both bishops along their long diagonals(c1-h6 diagonal or a6-f1 diagonal). This seems to be the most important benefit of e4/d4 IMO and not 'controlling the center'.


You are almost there-the point of e4/d4 is to decide how will you fight for the center which will directly decide what type of pace will that fight take. Since e4 gives free development of the pieces-but e4 pawn has no initial support-the emphasis in this types of positions is on speed. You must develop your pieces and rely on them to fight for the center. This usually leads to the scenarios described above under 1 and 3, second option being only seen in some variations of French defense and Caro-Kann. 

Since White has the advantage of the first move, he is naturally faster, so another benefit of the e4 is the ability for him to play gambits-hoping to be the first one to get the initiative in the center-which he can not achieve without controlling the center.Just the fact that some of the gambits in that link are viable, solid openings can show you just how much the importance of the center control is.

In short-e4 is played to give you fast development of your pieces-which is always used in fight for the center ( see Alekhine's defense, Ruy Lopez among many others ).

On the other hand, d4 is a bit clumsy move for developing pieces ( the queen does not have any good square to be developed ), but d4 pawn has support from the start.

This reduces Blacks options and immediate counter-attack is impossible. This gives White great solidity in the center but slows down his game. Again, the goal is the same-control the center but this time the strategy that implements this idea changes:

Instead of fighting the opponents pieces/pawns, that fight for the center, with your own, you will first occupy the center with pawns-so you can get space advantage.Once you do that you will have the time to finish development. Black, on the other hand, has a limited choice here. He can not counter attack at d4 at once ( 11. ... Nc6 is useless, opposing to 1. ...Nf6 in the Alekhine's defense ), so he usually opts for pressuring White center with his light pieces from distance, and then engineers a flank counter attack. The positions are usually closed, since White blocks center most of the time, but sometimes division of control occurs ( some variations of the Nimzo-Indian defense are a good example ) which results in semi-open games. 

To summarize:

Both moves are played with one thing in mind-to fight for the center. The only difference is in the way they implement the fight-with e4 you get speedy development but unstable center which results in a "fast paced" games, yet with d4 you get stable center which slows down the game.

In both cases Black and White fight for the center and the winner of that fight controls the center-which results in immediate advantage for him.

Since chess is a balanced game, if both sides play properly then nobody wins the fight, only one of the 3 scenarios listed above can occur.


  So while it may turn out that 1) e4 and 1) d4 give rise to good games for white I feel it may be more due to the rapid development which these moves allow rather than because these pawns 'control the center'.


Indeed. Just a small adjustment of your observation-quoting you:

So while it may turn out that 1) e4 and 1) d4 give rise to good games for white I feel it may be more due to the ability to beneficially deploy pieces to fight for the control of the center which these moves allow rather than because these pawns 'control the center'.


  Indeed, sometimes, these pawns can be an obstacle for white's own pieces.(I am looking at things from white's perspective but the same argument can be similarly posed from the black player's perspective as well.).


Exactly. The whole point of those moves is to enable other pieces to fight for the center. Which move you choose from those 2 is a matter of preference.

One thing for the end:

You can also fight for the center with light pieces only, making pawn thrusts later-after the position gets clarified and one such example is the Reti opening ( look at Reti's games to see what I exactly mean ).

Check out this section on Wikipedia( Control of the center ) and I think that this article also sheds some valuable light.

If you have further questions leave a comment-I will gladly help.


  Do post your thoughts on this.


You really should avoid discussions-here we strive for a single answer.

Best regards.