I came across this interview with Kramnik which was conducted back in 2005, but it’s an interesting read. He discussed all the world champions from Greco to Kasparov and made the following observation: “In my view, if you want to reach the heights, you should study the entire history of chess. I can't give any clear logical explanation for it, but I think it is absolutely essential to soak up the whole of chess history.”
Steinitz was the first to realise that chess, despite being a complicated game, obeys some common principles. He did not seem to understand dynamics very well.
Lasker was a pioneer of modern chess. Lasker had a lot of games that modern chess players could have had. I was not impressed with Tarrasch's play. He had imaginative ideas but like all players of that time he was prone to rigidity. We should not forget Rubinstein, an incredibly talented and fantastic chess player. Sometimes he created true masterpieces and was way ahead of his time.
Capablanca was a genius. I would not say he developed anything in chess ...He had a natural talent, which, regrettably, did not go hand in hand with hard work.
Alekhine also was a gifted player and had great talent. He had a strategic talent and was the first player who had a conscious feel for dynamics.
Euwe was a very good chess player. He realised how important the opening was and prepared it brilliantly. He was some sort of an "indefinable" player and his style is difficult to review. I have not grasped it to its full extent.
Botvinnik definitely represented a new era in chess. He was the first to realise that chess performance was not only dependent on chess skills. He developed comprehensive preparation for competitions which consisted of opening studies along with healthy sleep, daily routine and physical exercises. He grasped a number of conceptual things. Criminal as it may sound, I don't think he advanced chess, contributed anything absolutely new to the game. However, he made a great contribution to preparation.
Smyslov plays correctly, truthfully and has a natural style. I would recommend a study of Smyslov's games to children who want to know how to play chess because he plays the game how it should be played: his style is the closest to some sort of 'virtual truth' in chess. He always tried to make the strongest move in each position. He has surpassed many other of the World Champions in the number of strongest moves made. He mastered all elements of play.
Tal was a star, a real chess genius. As far as I am concerned he was not ambitious at all, he played primarily for fun and enjoyed the game. This attitude is totally unprofessional. But he was an incredibly gifted player and even with such an amateur approach, Tal managed to become a World Champion.
Careful study of Petrosian's games is required to form a clear impression of him. He was, so to speak, a very "secretive" player. We can call Petrosian the first defender with a capital D. He was the first person to demonstrate that it is possible to defend virtually every position. There is something mysterious about Petrosian. He was a brilliant tactician and an excellent strategic player, although his positional understanding was not as good as Smyslov's.
Spassky was the first really versatile player. I like his extensive and comprehensive play very much. I think he is a broad minded fellow who does not pay much attention to sundry odds and ends. Spassky's play reminds me of Keres. But Spassky has more fantasy and imagination than Keres who, in my view, had some problems with fantasy. Spassky was neither sufficiently disciplined nor ambitious.
What can I say about Fischer? At a certain moment he had everything: energy, drive, preparation, strong play, etc. as if all the rays were gathered together at one point! He had no weak spots at all - how can you handle such a person?! Fischer discovered modern preparation in the opening...he set tasks for his opponent at every move with either colour and in every opening. Fischer kept his opponent busy from the very beginning, he started setting problems from the very first move!
As regards other things, Karpov is a very strong universal player who is not so very different from the rest. His fighting skills are second to none. I think he did not pay attention to strategy.
It is always difficult to talk about Kasparov...he is a chess player who does not seem to have weak spots. At least, I don't know which weak point he had in his better days. Kasparov definitely has a great talent. There is nothing in chess he has been unable to deal with. The other world champions had something 'missing'. I can't say the same about Kasparov: he can do everything.