Many players unfamiliar with Reshevsky think he was a positional player; he wasn't.
The legendary Samuel Reshevsky (November 11, 1911 - April 4, 1992) was the most famous prodigy since Capablanca and he was the link between the pre-War and post-War era: he played Lasker, Alekhine and Capablanca and after the war, every great player from Botvinnik to Fischer. He played almost a hundred games with eleven world champions!
Everybody remembers what Fischer did to popularize chess in the 1970s, but in the early 1900s Reshevsky accomplished the same thing when, as a child, he created a sensation with his national tours. But when he stopped playing to complete his education, they stopped writing about him.
When Alekhine first met Reshevsky at the tournament in Pasadena in 1932 he wrote that his impression was most favorable. Reshevsky exhibited not a hint of arrogance and a quiet dignity. One wonders if Alekhine was as wrong about this impression as he was in his assessment of Reshevsky's play!
Alekhine observed that at that time, strength wise, Reshevsky was nothing special and was comparable to the "average American master." But what struck him was Reshevsky's style which "exudes utter tedium" and lacked imagination and if it wasn't for his obvious gift, Alekhine would have considered him as having a lack of talent! Alekhine believed that was because of Reshevsky's childhood being spent playing chess, resulting in, at the age of 21, his being like an old man, tired, disillusioned and incapable of creative thinking. Of course Alekhine turned out to be wrong as Reshevsky demonstrated a few years later at the 1938 AVRO tournament.
Reshevsky's weakness was his openings which he played almost entirely by intuition. Reshevsky claimed to have never studied chess, but that was not true. After Pasadena, for the first time in his life, he studied books on opening theory.
Botvinnik described Reshevsky's play as a forceful, active and impetuous adding that he evaluated positions in a routine, but unusual way. His main strength was his calculating ability. Botvinnik claimed that Reshevsky calculated only 2-3 moves deep, but he looked at a lot of possibilities. He stated this calculation didn't always help because there was no "purity" (not sure what that means) and he often ended up in bad positions. Botvinnik added that Reshevsky "had no taste" because he was willing to play any position at any time, but he skillfully complicated play and was not afraid of dangerous positions. He also played on both flanks and when he played a "waiting move" it generally indicated that he had realized his original plan wasn't going to work and he was awaiting a mistake and a convenient opportunity.
Reshevsky also liked to make harassing moves and to force his opponents into difficult situations where he could use his imagination. Also, he was always ready to go into the ending, especially those with a lot of pieces, because in those positions he had great skill.
According to Botvinnik, Reshevsky's weaknesses were his weak positional feeling in complicated positions, openings and his routinely getting into time trouble. In time trouble his play was "deft" but he did make oversights.
Reshevsky's serious battle for the world championship essentially ended in the 1953 Candidates Tournament. True, in 1968 he played a match against Korchnoi to see who would move on in a bid for the world championship, but by that time he was no longer truly a serious contender.
Even after the 1953 tournament he continued to unnerve the Soviet players for some time to come, especially after he inflicted a painful defeat on Botvinnik in the 1954 US vs USSR radio match.
In the summer of the following year when the US team was in Moscow for a return match. Reshevsky, bypassing FIDE, actually proposed a match with Botvinnik for the world championship. Botvinnik told Reshevsky he would let him know, but Reshevsky never heard from him, adding in a 1991 interview that, "I have nothing against Botvinnik."
Bronstein wrote that Reshevsky was always sure that he played chess better than anyone in the world. He also revealed that after the Moscow team match the American ambassador held a reception at his residence and Soviet Premier Nikita Khrushev was in attendance. Reshevsky boldly asked Khrushev to allow him to play Botvinnik a match for the championship and Khrushev replied that he wasn't the one who could make that decision.
Nobody in the Soviet chess federation wanted to risk a match, but they did invite Reshevsky to play a 24-game match against Bronstein. The match was due to take place in December, 1956 with 12 games in Moscow and 12 in New York with a $6,000 (around $53,000 today) prize fund. Unfortunately, the October, 1956 Hungarian revolt caused the match to be canceled.
Viktor Korchnoi wrote that in every game Reshevsky played you could sense his enormous desire to fight and win. While his lack of opening knowledge was a handicap, in the middlegame he was extremely confident and had enormous tactical talent and psossessed the ability to make original and non-routine (there's that description again) evaluations. Positional battles were not to his taste and he avoided positions where maneuverings and waiting were required.
Kasparov, on the other hand, made the observation that Reshevsky did have a high level of positional understanding or else he would never have maintained such a high level of play for so many years.
In the Match of the Century in 1970, Reshevsky was assigned 6th board in a secret vote by the other players. In that match he made an equal score against Smyslov, but had to sit out the last game for religious reasons. His replacement, Olafsson, lost to Smyslov which could have been the reason for the Soviet's narrow one point victory in the match.