Many people are interested in differences between the brains of males and the brains of females, and differences between males and females in IQ tests and memory tests. A careful examination of this area provides some evidence against the claim that the brain is the source of human intelligence, and the claim that memories are stored in synapses of the brain.
The brains of males are significantly larger on average than females -- about 10% bigger. But we know that females tend to be shorter and weigh less than males. Some say that the relative size of female brains (female brain sizes compared to female body sizes) is no smaller than the relative size of male brains. But in a scientific paper a scientist states, "After correcting for body height or body surface area, men's brains are about 100 g heavier than female brains in both racial groups." That difference of 100 grams is about 7% of the total weight of a male brain (about 1350 grams).
So using the idea that the human mind is produced by the brain, we should expect that males do about 7% better at school and about 7% better in IQ tests. But this is not at all the case. Males and females do about the same on IQ tests, with a difference of less than 1% or 2%. In the United States females tend to get just as high academic grades as males. In this regard, the claim that the brain is produced by the mind fails the observational test.
Now let's consider human memory. The standard academic dogma (unsupported by any facts) is that memories are stored in the synapses of brains. The persistence of this dogma is mystifying, given what we know about the instability of synapses. Humans can reliably remember things for longer than 50 years, but individual synapses do not last for years. The proteins that make up synapses are very short-lived, having an average lifetime of only a few weeks.
Wikipedia.org states, "Multiple studies  have found a higher synaptic density in males: a 2008 study reported that men had a significantly higher average synaptic density of 12.9 × 108 per cubic millimeter, whereas in women it was 8.6 × 108 per cubic millimeter, a 33% difference." The 2008 study mentioned is the study "Gender differences in human cortical synaptic density" you can read here.
Now, this 33% difference is quite a big difference, much bigger than the brain size difference previously mentioned. Under the assumption that synapses are the storage place of memory, we should expect (given this 33% greater synapse density in males) that either males tend to have stored much more memories than females, or that males are better at remembering things than females. But such things are not true.
There is no evidence that males store more memories than females. One good way of testing whether males store more memories than females is simply to look at academic scores. If males tended to store more memories, they would tend to have higher academic scores than females. But females do just as well as males in tests of learned information.
Below is a quote from an article in the New York Times indicating that boys do not do better than females (on average) in school tests:
"The study included test scores from the 2008 to 2014 school years for 10,000 of the roughly 12,000 school districts in the United States. In no district do boys, on average, do as well or better than girls in English and language arts. In the average district, girls perform about three-quarters of a grade level ahead of boys. But in math, there is nearly no gender gap, on average. Girls perform slightly better than boys in about a quarter of districts...Boys do slightly better in the rest."
Here are some quotes from the scientific paper "The Role of Sex in Memory Function: Considerations and Recommendations in the Context of Exercise":
"Females tend to outperform males in episodic memory function....Females tend to perform better than males in verbal-based episodic memory tasks, as opposed to spatial-based memory tasks . Females generally access their memories faster than males , date them more precisely , and use more emotional terms when describing memories . Superior verbal memory for females also appears to be independent of intelligence level . Additionally, females also have greater specificity for events imagined to occur in the future . In general, females outperform males on autobiographical memory (particularly with high retrieval support via verbal probing ), random word recall , story recall , auditory episodic memory , semantic memory (driven by superiority in fluency) , and face recognition tasks [10,17]."
So the paper is telling us that female memory performance is better than male memory performance in all these areas. But how can that be, if males have a synaptic density 33% greater? We have here additional evidence that there is no truth in the common claim that memories are stored in human synapses.