Q: Does the number 40 have significance in Hebrew mysticism?
A: The number 40 is of great significance, not only in mysticism, but also in the simple understanding of the Torah. For example, the 40 days that Moses was in heaven to receive the Torah, 40 days of the Flood. In addition, 40 relates to the 40 days from the beginning of pregnancy until the fetus is well formed. This is a very important stage in pregnancy.
40 is also the value of the letter mem, which means water. This is why 40 refers both to the Torah, which is water, and also to the Flood. In the future the flood will be a positive concept–the flood of knowledge of G-d. This is the inner soul of the Torah which will fill the earth just as water covers the seabed. Water covering the seabed is the secret of the letter mem and the number 40.
In addition, when one becomes 40 years old he receives the deepest measure of understanding, in order to understand the Torah. This is especially in order to understand the deep intention that his teacher had that he was not able to comprehend initially. At the age of 40 one understands his teacher's inner meaning.
It would be most worthwhile for you to see the Hebrew Letters Book on the letter mem, which provides more information on the number 40.
Wishing you much success in your further studies.