Many people believe that if you shave or - especially - wax your legs, arms, chest, pubic hair or armpits then the hair will grow back stronger, or thicker, or more black, or more rapidly, or any combination of those.
Is it actually true?
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According to a Mayo Clinic dermatologist, no, it is a myth.
Both he and snopes.com point to the fact that after cutting or otherwise removing hair, it grows back in feeling coarse and stubby to the touch. This can lead to the perception that the hair is stronger or thicker, when in reality, it's the same as it always was, just shorter and with rougher ends. After the hair grows out again naturally, the hair will likewise seem smoother, because hair tapers when not cut.
Short answer: No
Here is a study from the Journal of Investigative Dermatology:
The effect of repeated shaving on human hair growth was studied. Five healthy young white men each shaved one leg weekly for several months and left the other leg as a control. No significant differences in total weight of hair produced in a measured area, or in width or rate of growth of individual hairs, could be ascribed to shaving.
According to this list of myths there are other studies that confirm the findings (although it does not contains citations from or links to the studies)
However, what some young individuals can find in their daily lives can seem to counter that claim. If an adolescent shaves their hair and waits for it to grow back it may indeed grow back thicker than before because the individual is going through puberty and their hair thickens with time. This has nothing to do with shaving but can fool an adolescent that it does. If they keep shaving their hair a long time can elapse until they see their hair fully grown out again. After they do they may rightly assume that it has gotten much thicker than before and accredit it to the shaving.
This could possibly be how the myth originated.