His accomplishments are just too many to list here so I'll just say: Anatoly Evgenyevich Karpov, one of the greatest of all time.

The players who might be a bit lost in history are the gallery of one-two year champions that FIDE somehow manufactured in the years that followed Kasparov's leaving FIDE. It has only gotten straightened out in the last few years, where Anand is recognized as undisputed world champion.

Karpov's greatness is as solid as gold.

Karpov and Kasparov, by contrast, were like Tal. They appeared out of nowhere and vaulted to the top on their very first try. It's great, but it's not as good a story.

We are reaching the point, however, that the majority of players today were not living when Fischer played and soon Bobby will take his place alongside Capablanca and Lasker as an historical figure.

<When having an edge, Karpov often marked time and still gained the advantage! I don't know anyone else who could do that, it's incredible. I was always impressed and delighted by this skill. When it looked like it was high time to start a decisive attack, Karpov played a3, h3, and his opponent's position collapsed.>

St Karpov, St Kasparov.

Like Kramnik said, Karpov had the great talent of making the smallest, most subtle moves, that somehow won him the game.

<You may have some problems understanding the inimitable Alexander Roshal, who knew just a couple of hundred words of English, but used these better than anyone with a similarly limited vocabulary. Alexander was a trainer at the time of their meeting, a 2430 rated master, who played some blitz games against the 11-year-old chess prodigy Anatoly Karpov – with his students crowded around. Roshal tells us that while normal prodigies will sacrifice pieces and tear you to pieces, the young Karpov was different – "he would not give you a single pawn, not even a single square." After he had lost the first game against Karpov, Roshal asked the students around him to tell him what he had done wrong – turning the game into a didactic lesson for them. After losing three more he again asked his students to identify the mistakes he had made. "Why did I lose?" he asked. From Karpov came the timid suggestion: "Perhaps because I am a better player than you?">

I can see it. Great material for Hollywood for many decades. AK as Anthony Carp from an honest family of farmers in the heart of Kansas, married young to his high school sweetheart, Dory Gale. I can also see Gary Caspar emerging through sheer willpower and determination from the depths of hardship, abandoned by his father (a cattle-wrangling brawler and drunk in the Casper, WY area, who abused him as a child). Now we throw Capablanca in the mix by moving his birthplace to Manhattan. Here he is, Mr. Joseph-Raoul Whitecape, a very trim, suave early century New Yorker from a family of means. You have covered the main pillars of the American landscape, and you have all the perfect ingredients for a Chess Holy Trinity lasting longer than Christianity itself. Now we turn Fischer into an unstable misfit from a Budapest ghetto, with a funny Hungarian name, and let’s make movies.

What he said.

http://whychess.org/en/node/1778

Yes, you're right. What should have happenned was that they should have kept playing, then it would have been patently obvious that Kasparov could still play chess at that point, but Karpov could not. Then Kasparov would have won the match in 1984.

He's the only player with the rightful claim of being No. 2. Only Kasparov edges him out.

I'd say that there was one great player who proved him wrong.