As a teenager and an undergraduate, I sometimes experienced an unusual mental state when studying mathematics. This was a state of great happiness and seemed to arise when I was engaged in deep, deductive thinking – for instance, after spending days or weeks attempting to prove or disprove some mathematical statement. The state only arose when I was doring pure mathematics – ie, the theory of mathematics, not its application. It never lasted long – perhaps an hour, at most – and only happened a few times a year. The state did not always arrive, and I never determined what in particular I did, if anything, to provoke it. It was one of the key reasons that I decided to major in pure math at university. For ease of reference, I will refer to this state as one of deductive bliss.

I experienced no dreams or visions or other sensory hallucinations in this mental state. I was always conscious throughout and the state was not what is commonly called a flow state. I was (and still am) very familiar with flow states, and can reliably achieve a flow state after only a few minutes playing a keyboard. One difference between the two states is that during a flow state, I am usually not very aware of my surroundings; in the state of deductive bliss, however, I was still quite aware of my sensations and my surroundings. Another difference between the two is that the deductive bliss state was always immensely pleasurable, whereas (for me, at least) flow states, while enjoyable and not in any way unpleasant, lacked such intense happiness. The mental state was one that can only be described as bliss, taking exceptional pleasure in the operation of deductive inference. (I realize that this may sound strange to many people.)

Not pursuing a career in mathematics, I had forgotten that I ever had these mental experiences until during the Pandemic in 2020. Then, in the first lockdown, I started learning Ancient Greek. As I learnt and practiced the grammar of AG, I again experienced this state of deductive bliss. As is well-known, Greek grammar has a structure making its application akin to mathematical deduction. (If you believe that language and culture may influence one another, there may be a connection between the deductive grammatical structure and the strength of classical Greek mathematics.) Just as in my earlier experiences, the onset of this state happened only rarely and without any deliberate intent on my part.

I have now had this state of deductive bliss on a third type of occasion – when listening to a live performance of a work of music. The music in question was Rachmaninov’s First Piano Sonata, in D minor (Op. 28), and the performance was that of Mr Alexander Doronin in the Semi-Final Round of the 2025 Hong Kong International Piano Competition. Before this occasion, I had heard that Sonata performed in recital several times (by Maestro Dmitri Alexeev, Mr Kasparas Mikuzis and Mr Doronin himself), listened to online recordings, and studied the score a little. Hence, this is a work which my mind knows something about (although not as much as it would do were I to learn to play it myself). Like much art music, there is an internal logic to the work, a logic which may be considered deductive – at least, deductive within its own universe. As before, the state did not last long – only about 30 minutes, beginning the final movement and continuing beyond the end of the work for about 15 minutes.

I am surprised and intrigued that I should enter a state of deductive bliss when I listen to any music. It would be delightful to discover how I could engineer its onset, such is the great happiness I experience.

Acknowledgments

I am grateful to discussions about these experiences with AD, as well as with VN, DKM, LB and CC. A recording of the live stream of Mr Doronin’s performance is here (from minute 1h17).