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Mambo is a Latin dance of Cuba. Mambo music was invented during the 1930s by Arsenio Rodríguez,  developed in Havana by Cachao and made popular by Dámaso Pérez Prado and Benny Moré. the In the late 1940s, Perez Prado came up with the dance for the mambo music and became the first person to market his music as "mambo". After Havana, Prado moved his music to Mexico, where his music and the dance was adopted. The original mambo dance was characterized by freedom and complicated foot-steps. Some Mexican entertainers became well known dancers like Tongolele, Adalberto Martínez, Rosa Carmina, Tin Tan and Lilia Prado. Most of these accompanied Prado in live presentations or were seen in Mexican films.
The original form of the dance and music are alive and well in Cuba and in taught in dance studios in Mexico City. An example of authentic Mambo dance can be seen in the film The Motorcycle Diaries.
Mambo on 2 
The Mambo dance that was invented by Perez Prado and was popular in the 1940s and 50s Cuba, Mexico City, and New York is completely different to the modern dance that New Yorkers now call 'Mambo', which is also known as Salsa "on 2". The original mambo dance contains no breaking steps or basic steps at all. The Cuban dance wasn't accepted by many professional dance teachers. Cuban dancers would describe mambo as "feeling the music" in which sound and movement were merged through the body. Professional dance teachers in the US saw this approach to dancing as "extreme," "undisciplined," and thus, deemed it necessary to standardize the dance to present it as a sell-able commodity for the social or ballroom market The modern dance from New York was popularized in the 70s by Eddie Torres and his contemporaries who were 1st or 2nd generation Puerto Rican immigrants. This style is not danced to Mambo music, for which it is poorly suited, but instead to Salsa music.
The Eddie Torres version of Mambo (or Salsa On 2) was actually developed by dropping the chase from cha cha, when the music became too fast to diligently carry out the chase as a technique. Since the forward break is on 6 it would suggest that the cha cha from which the dance was derived was 1) counted in 4s not 8s and 2) was started with the back break and not the forward break. So, arguably, it is actually On 6 (if you take the beat the forward break is on as the datum). Note, all aspects of the moves are shifted more than one beat which also gives the hint it is missnamed.
Ballroom version of Mambo forward breaks On 2, with a pause/chill on the 1 beat. This makes more sense as all aspects of the moves are then shifted up only one beat.
See also 
- Garcia, D. F. (27 November 2007). "Going Primitive to the Movements and Sounds of Mambo". The Musical Quarterly 89 (4): 505–523. doi:10.1093/musqtl/gdm006.