The answer is no! Why? Man appears to have a set of fantasies and illusions during the period in which he sleeps, which come in the form of dreams, as many people have worked on the study and interpretation of dreams since ancient times, which were believed in the past to be a message to the person who dreamed of them from God in order to tell him about a specific thing or that It sends these dreams to the person in order to give him information, and this is what was interpreted with regard to the topic of dreams among the Greeks, and other than ancient civilizations. (Freud) So he said that dreams are a set of desires and wishes that a person desires to achieve in his life and from the intensity of his love and his attachment to these desires, they may come to him in the form of a dream as a result of repeated and continuous thinking about these wishes, which leads to the merging of these thoughts with dreams, while (Carol) Young) in another interpretation, which is that dreams come to the person as a warning to him and give him solutions to the problems that he may go through. As for the Muslim scholars, they have prepared special books on dreams while finding a religious interpretation for them, such as Ibn Khaldun and Ibn Sirin. Evil or to order him to do a certain thing in it that is good for him, and the dream that comes from Satan, such as nightmares and dreams, is about what a person wants to achieve and aspires to, and this is what the Muslim scholars have relied on and relied on to interpret dreams, in addition to the hadiths of the Messenger, may God bless him and grant him peace and verses. The Holy Quran.
We often dream about our work, so why should mathematics be exempt from dreams? There are some credible claims of mathematicians whose contributions originated in dreams, Descartes and Ramanujan among them. Considering your question at face value, it would depend on the dream, how deeply the problem has taken root in one’s thoughts, and one’s talent at analysis related to the problem. I would say yes, there is a possibility that your interest in fractional derivatives is driving your dreams, and that the dreams could be relevant.
The answer is no. Most of the dreams coming are actually the thoughts we hve in mind after thinking hard on it when we are awake. There are some credible claims of mathematicians whose contributions originated in dreams, example: Descartes and Ramanujan . Considering your question at face value, it would depend on the dream, how deeply the problem has taken root in one’s thoughts, and one’s talent at analysis related to the problem.
Sourangshu Gosh, you have copied my key phrases and arrived at "no" instead of "yes". When you steal my thinking I suggest that you come to the same conclusion. You are now wrong as well as unethical.
Although I am not an expert on the subject, I believe in science can answer the question affirmatively. To perform such an examination:
1) Determine a sufficient number of volunteers (mentally healthy people without illnesses like Alzheimer's disease).
2) You should determine the psychological conditions of these volunteers that deeply impressed them (Here I am talking about the past experiences; of course you should collect sufficient information in the long term and in the short term separately).
3) Continuously, you should gather and record the electroencephalogram (EEG) and electrocardiogram (ECG) signals of the volunteers during their sleep.
4) If possible, you should record their faces during sleep. Thus, you can find out their emotional and spiritual condition through image processing. (As far as I know, this is an existing technology emerging for security reasons)
Of course, it is possible to increase the number of these suggestions. Maybe, you can also record their dreams by asking them after the night.
After collecting sufficient statistical data, a comprehensive analysis may be performed. Then, you can propose a mathematical model via a holistic approach. Thereby, you may predict at least some pieces of information regarding the night dreams. However, it is still hard to know about the contents of the dreams. This is beyond my expertise and imagination.
I hope this answer has provided some inspiration for you. I wonder about the results of your study.