I got this random science fact from my mobile carrier.
Once a human reaches the age of 34, he/she will start losing approximately 7,000 brain cells a day. The cells will never be replaced.
Is the above claim true?
The claim is not true; neurons continue to form, and the connections between them to change, throughout our lives.
This paper on neurogenesis (i.e. forming of new brain cells) opens with this sentence:
It is now well documented that active neurogenesis does exist throughout the life span in the brain of various species including human.
However, it is true that the rate of forming new cells slows down with age. Here is a quote from a webpage of a lab dedicated specifically to researching neurogenesis:
The brain continues to produce new neurons throughout life; however, the Bartlett laboratory has shown that the rate at which these new nerve cells are produced declines with age and may contribute to age-associated memory loss.
I found no sources for the age of 34 to be critical, but in my experience a reputable neuroscience paper would never give a statement like that, because a myriad of additional factors are likely to be involved.