The term “cognitive formation” (also referred to as cerebral or neurobiological formation) reflects an assumption that cognitive abilities can be maintained or enhanced by exercising the brain, by analogy with how physical fitness is enhanced by exercising the body.
Although there is strong evidence that aspects of brain structure remain plastic throughout life and that high levels of mental activity are associated with reduced risk of age-related dementia, Scientific concept for the concept of “brain fitness” is limited. The term is practically never used in the scientific literature, but is commonly used in the context of self – help books and commercial products.
Cognitive Reserve is the ability of a person to respond to the various cognitive demands of life and is evident in the ability to assimilate information, understand relationships and develop reasonable conclusions and plans. Cognitive training is an assumption that certain activities, carried out regularly, could help to maintain or improve the cognitive reserve.
Beginning in 2016, companies offering products and services for cognitive training marketed them to improve academic performance for children and adults, improving memory, processing speed and problem solving, and even In the prevention of dementia or Alzheimer’s disease.  They often support their marketing with a discussion about the academic or professional background of their founders, some discussing neurosciences that support their approach, particularly the concepts of neuroplasticity and transfer of learning, and some cite evidence of ” clinical tests.
Beginning in 2016, there was evidence that some of these programs have improved their performance on the tasks to which users have been trained, less evidence that performance improvements are spreading to related tasks and almost no evidence that the “Brain training” is a generalization of cognitive performance every day; In addition, most clinical studies were erroneous.
Cogmed was founded in 2001, Posit Science in 2002, and Brain Age was first published in 2005, while taking advantage of growing public interest in neuroscience, as well as increased parent ADHD and other learning disabilities in their children, and worry about their own cognitive health as they age.
The launch of Brain Age in 2005 marked an evolution on the ground, as these products or services were marketed to relatively narrow populations (for example, students with learning disabilities), but Brain Age was marketed for all , With a large media budget.  In 2005, US consumers spent $ 2 million on cognitive training products; In 2007, they spent about $ 80 million.
To address the growing public concern about aggressive online marketing of brain games to the elderly, a group of neuroscientists published a letter in 2008 that warned the general public that there was a lack of research showing The effectiveness of brain games in the elderly.
In 2010 the Agency for Research and Quality of Health Care revealed that there was insufficient evidence to recommend any method of preventing age-related memory deficits or illness, Alzheimer’s disease. [ten]
By 2012, “brain training” is a $ 1 billion sector and is expected to reach $ 6 billion by 2020.  In 2013, the market was $ 1.3 billion, Software accounted for about 55% of these sales.  At that time, neuroscientists and others were increasingly worried about the general trend of what they called “neurofiche”, “neurohype”, “neuromania”, neuromyths.
In 2014, another group of scientists issued a similar warning.   Later in the same year, another group of scientists made a contrary statement , organized and maintained by the Chief Scientific Officer of Posit. 
As of January 2015, the Federal Trade Commission (FTC) has sued companies that sell “brain training” programs or other marketed products to improve cognitive function, including WordSmart Corporation, the company that manufactures Lumosity and Brain Research Labs (which sold food supplements) for misleading advertising;  Later this year, the FTC also sued LearningRx.
The FTC found that Lumosity’s marketing “preoccupied consumers” fears age-related cognitive decline, suggesting that their games could avoid memory loss, dementia and even Alzheimer’s disease, “without providing any evidence To support its claims. The company was ordered not to claim that its products can “improve” performance at school, at work or in athletics “or” [delay or protect] against decline related to the age of memory Or other cognitive functions, including a mild cognitive deficiency, dementia or Alzheimer’s disease “, or” [reduce] cognitive disorders caused by health conditions, including Turner’s syndrome, Post-traumatic stress disorder (PTSD)
As part of its lawsuit against LearningRx, the FTC stated that LearningRx had been “deceptively asserted  that their programs were clinically proven to permanently improve severe health problems such as ADHD (Attention Deficit Hyperactivity Disorder ), Autism, dementia, Alzheimer’s disease, stroke and concussion. ”  In 2016, LearningRx settled with the FTC by agreeing not to make the contested claims unless they had “competent and reliable scientific evidence” that was defined as randomized controlled trials Carried out by competent scientists. For the monetary component of the judgment, LearningRx agreed to pay $ 200,000 of a $ 4 million settlement.