1d4 Nf6 2c4 e6 3Nf3 b6 4g3 Ba6!? and earlier in books they wrote that 5Bg2 was bad, gave away a pawn... but, now computerprograms find it's ok and also very good to play 5Bg2. Funny, isn't it?

Forgot to write that it's some alternative moves if you use "move list". It's of course a lot of better moves for black than I shows here, but white is not worse after 5Bg2 anyway, and that's the point.

I share your feelings about this discovery.  It is true that all of white's methods of defending c4 are awkward.  So why not sac the pawn?  I am trying to imagine Nimzovich himself writing about this issue.  He would say something along the lines of:  Black's attack on the c4 pawn is fully justified.  Even the powerful silicon minds cannot find a way to defend c4.  The pawn and the very square on which it stood come under the grips of black's army.  The naysayers have been proven wrong!

Question.

Why doesn't black play 12...pawn takes bishop e4?

Thanks.

Mainline is 5. Qc2. White can hold the pawn. Also I feel that black would be fairly comfortable after 6...Be7. 

It's a lot of ways to try to defend the pawn. Qc2, Qb3, b3, e3 and Nbd2. But it was not correct in books to write ?? after 5Bg2. The silicon minds have proved that white have full compensation for the pawn, and in some cases advantage for white.
To Bondiggity: I guess black can play both 6-Be7 and 6-h6 in that position.

If 12-pawn takes bishop, queen take pawn and threats on both f7 and a8.

Yes it is amazing how programs will sac pawns for active considerations.  Instead of defending c4 awkwardly, white lets black capture awkwardly on c4.  Nimzovich's strategy was to exploit the c4 square in the Nimzo- and Queen's Indian Defences, but did he realize that it was in the bargain that he might have to actually carry out the threat of taking c4?  It goes to show that the threat is often stronger than the execution.  In this case, black's threat to c4 has for many years provoked moves such as b3, but when black is asked to carry out his threat it is not so deadly after all.

How does this prove anything. All this proves is that white played poorly. I mean really moves like 10...b4?? being include to prove the worthiness of an opening line. There are reasons why only like 15 games where played with this line in master games, with much higher success for black. I fail to believe that this analysis is unbiased. 

d5?  Why god would you play d5?  As shown Nd5 refutes it immediately.  Play Be7 to allow Bd5 in reply and black is slightly better.  Also interesting is Bd5!? immedaitely and Bb4+!?

This is not analysis, analysis contains best moves by both sides, it does not contain one side making good moves, and another side making reasonable looking but bad moves.

It's a lot of lines, but can't take them all now  But I was surprised that the silicon minds found very fast that it was compensation, and white and black was equal after 5Bg2, even Bxc4 is a pawn up. But, and it's a big but, white must play accurately to get compensation for the pawn. So it's easier for black to get advantage, than for white. 

 OK. Thanks for explaining. I see it now.

I think that this is a very interesting comment. Opening gambits in general have over the centuries been developed by humans, and they give easy, quick development and usually pretty obvious play.

Using pawn sacrifices suggested by computers is dangerous, because although it might be sound, you're totally right that the player sacrificing the pawn might have to reel off a whole sequence of moves *just* to have sufficient compensation for the pawn.

Practically speaking, it might be likely that humans playing that line might end up simply worse without enough compensation for the pawn, because they don't play with the accuracy of a computer.

I'm not necessarily saying this is the case here, but it's worth thinking about when evaluating computer-suggested gambits in the opening.

 But there really isn't anything wrong with b4.  It forces the exchange of the knights on the next turn, which simplfies matters greatly for black.

It gives up a central pawn on the spot. 

Two times I sent diagram, but it stands "you must send a comment". I try this for 3rd and last time now, with this text first. Use "move list" to see some alternative moves below: