[1] Burman was born in London, England, on December 11, 1898, to a large Jewish family of six children, who emigrated to the United States in his early youth.

[2][3] He lost to Johnny Ertle or Ertel, a disputed claimant to the world bantamweight championship, on November 21, 1917, in a ten-round newspaper decision at the Arcadia Rink in Milwaukee.

[4] He lost to 1922 world junior featherweight champion Jack "Kid" Wolfe in a close ten-round newspaper decision in Buffalo, New York, on January 23, 1920.

Wolfe, a slightly awkward boxer, but powerful hitter, carried a strong punch with his right which he delivered well in the fourth, sixth, ninth, and tenth rounds.

In the ninth and tenth, after the boxers were warned against clinching, Wolfe found openings to score sufficiently against Burman to take the decision.

Both boxers, being evenly matched, clinched frequently throughout the bout and were forced to fight at close range, displeasing the vocal crowd.

[5] In two other meetings with Wolfe, in the prior two months, Burman was unable to win a newspaper decision, scoring one draw and another loss.

In an important victory on September 6, 1920, Burman defeated reigning world bantamweight champion Pete Herman in a non-title bout at the Colliseum in St. Louis in an eight-round newspaper decision.

According to the Chicago Tribune, Burman defeated 1919 world bantamweight champion Jackie Sharkey in New York in a ten-round no-decision bout on June 19, 1917.

Burman, who was known as a good outside fighter, scored with left jabs and right crosses, while Sharkey, with a slight disadvantage in reach, dominated the infighting.

[9] Burman met Sammy Sandow, another Jewish boxer with Russian ancestry, and won a ten-round newspaper decision on March 31, 1922, in Detroit.

In his most important contest, Burman was scheduled to fight a rematch with bantamweight champion Joe Lynch at Madison Square Garden in a rare title match on October 19, 1923.

Though nearly blinded by a gash above his eye, Goldstein held Burman to a draw in points in the final two rounds, which strongly aided the judges in awarding him the decision.

Burman defeated Johnny McCoy (who would become the 1927 world flyweight champion), on December 21, 1923, in a late career ten-round newspaper decision in Blue Island, Illinois.