With many fellow-musicians in the audience, including his friend Yo-Yo Ma, pianist Emanuel Ax outdid himself in eloquence, depth, and sheer sonorous glory Sunday afternoon at Jordan Hall. Sponsored by the Celebrity Series of Boston, Ax’s recital focused on fantasies, calling fresh attention to the magic aesthetics of in-the-moment improvisation in Beethoven, Schoenberg and Schumann. Not only did Ax reveal the deeply focused emotionalism of Schoenberg to us, he also revealed deep personal insight with Beethoven’s well-known Piano Sonata No. 14.

“Only a genius may reign freely” remarked Schumann (cited in the concert’s program notes), corroborating the testimony of Baroness Dorothea von Ertmann, who once related to Felix Mendelssohn how Beethoven had consoled her after she lost a child. Beethoven invited her to visit him, sat down at the piano, and said, “Now we will converse in music.” For more than an hour he improvised for her. “He said everything to me,” Ertmann wrote to Mendelssohn, “and finally gave me consolation.” This power of improvisation, the direct expression of inner emotions in the language of music, formed the heart of Ax’s program.

Beethoven’s two Op. 27 piano sonatas are marked “quasi una fantasia”, which literally means “almost a fantasy”. But as an instruction to the performer it means that they are to be played in the manner of an improvisation, the usual sonata forms not necessarily followed, and the movements are to be played without interruption.

So it is not surprising that the Op. 27 No. 1 opens with an Adagio five-part rondo. Ax started with a light and pearly touch, suggesting an inner search for pitch and voice flourishing into a tentative bel canto crescendo. It matured into a sweeping motion as the sense of the inspired musical idea gained its footing, with Ax decoupling his two hands into two distinct pianists interacting and communing with each other, opening a multi-dimensional space. In the return of the A section, Ax turned this dialogue into pure beauty, implying that inspiration gets its affirming feedback in the astonishing human capacity for aesthetic rapture. (What is beauty? Why does it move us? What is it about our sensorium that makes us recognize it when we hear it?)

Ax gave the two-minute Scherzo a dynamic contrasting of momentum and surface sparkle, again uncoupling his two hands to force the dark restlessness of drive to penetrate lightness and subvert stability, leading directly into the Adagio, where suffering was unleashed and transformed into beauty, somber and sublime but crowned with ecstatic trills that brought so much psychic refreshment that Ax was able to lead us organically into the vivacious, “unbuttoned” final Allegro. Here he revived the dialogue of earthy opacity and surface sparkle, turning the sparkle into determination, tinged with humor and defiance. Improvisation as self-portrait. Beauty as self-therapy, as a radically personal struggle with despair.

Schoenberg (whose marvelous self-portrait of 1911 is on display right now at the Harvard Art Museums) composed his Three Piano Pieces. Op. 11 during a time of great anguish brought on by his wife Mathilda’s affair with their friend, the painter Richard Gerstl, who took his own life when Mathilda returned to Arnold and their children. Schoenberg’s Op. 11 pieces represent his final break with tonality, but as Ax told us in an introduction, “atonality does not mean lack of feeling. There is everything from fury to yearning, just as in Mahler.” Ax approached Op. 11 as a sort of triptych. He imbued the first piece with a subdued, dreamy attempt at self-soothing, interrupted by inspiration in a motif seeking to draw the self out of oblivion. The same call to the unbearable lucidity of consciousness rang out in the second piece, forcing the self out of a soothing ostinato in order to breathe the “air from another planet.” Ax concluded Op. 11 with a chaotic and expansive third piece hurled into the galaxy, uncentered but not the least bit unhinged, with Ax drawing power from darkness as from a cosmic wellspring of Night.

Ax demonstrated the fullness of his prowess with Beethoven’s Sonata No. 14.  We thought we knew that ‘other’ quasi-fantasy! Ax got rid of the moonlight that a publisher abusively attached to it. Focusing on improvisation, Ax made this writer imagine an intimate and staggering self-portrait of Beethoven’s inspiration and daily work. In the delicacy of the opening ostinato triplets, one kind of vision emerged out of the composer’s hyper-listening and total concentration, growing organically out of hidden, germinating seeds with all of the ascending mystery of organic life. In the Allegretto, Ax used sharp accents on the beat and strong syncopation in the trio section to depict the composer’s constant fretting with scores and deliberate efforts to shape musical ideas into intelligible physical scores, tinged with frustration. But then! Genius, like love, strikes unexpectedly, at the speed of light, swooping down on the composer’s soul like a fierce and sublime eagle. Ax held nothing back in the presto agitato, insistently bringing forward the overwhelming, intoxicating, overflowing flood that Beethoven poured out again and again in its sublime jaws or towering motion ― out of all proportion with human means and capacity, forcing the composer to struggle alone with an allure so profound and so all-encompassing that it might annihilate him in the process. Wow. Moonlight? Please. Had I experienced that sonata for the very first time? Famously respectful to scores and often seemingly self-effacing before composers, Ax unbuttoned himself to unveil the full magnificent fertile and creative tragedy of Beethoven’s sacrifice.

Ax introduced the second half by contrasting Schoenberg’s Six Little Piano Pieces, Op. 19 (unlike Op. 11), as distinct, autonomous “moments of emotion” that embody Schoenberg’s “experimentation with miniaturization.” He gave the brief first piece, marked “light and delicate” the feel of being solicited out of nowhere by a musical idea, then conveyed in Piece II that the inspired idea has a life of its own, unexpectedly shimmering and liquid. Piece III made us (or at least me) hear the aesthetics of doubt — wonderfully undermining resolve and vivifying creativity. In IV, I heard Fate, the Implacable — how do I skirt it? In V, I heard the aesthetics of Light, how it curls and shines suddenly by its absence. In VI, composed as a “tombeau de Mahler,” I heard a magic “moment of time”, the will-to-memory that music is, keeping inspiration alive and passed on from composer to composer open-endedly.

So what did Ax reveal to us about inspiration in Schumann’s Fantasie, Op. 17, composed in the dreadful year in which he had “renounced” Clara forever? With gorgeous lyricism, Ax showed us how Clara turned into the Immortal Beloved within, sublimed through renunciation into an inexhaustible source. Their legendary love forever inspired heavenly heights, transcending loss. Ax approached the middle movement march softly and gently at first, before quickly bringing it to a swell, emphasizing the psychic interiority of Florestan’s birth; out of the renunciation of Clara he turned her into his North Star. She now provided him with both the energy, independence, and the self-confidence to honor Beethoven as Liszt requested, as well as the self-confidence to stand shoulder-to-shoulder with Beethoven and Liszt! Ax in turn imbued the final movement with hymn-like serenity, unveiling the birth of the tender and introspective Eusebius as an inner search for the absent Clara hidden deep within his heart. We heard the aesthetics of Yearning and Absence, as Eusebius descended through deep chords deeper and deeper into himself to retrieve Clara from the Underworld. But as his faith in her empowered him not to look back, her voice appeared and grew in lyrical motifs and she subtly turned into Beatrice guiding him to a heaven of stars.

Responding to a rousing ovation, Ax capped off the evening with the lyrical, warm, and lush Schubert Lied Ständchen (Serenade) in Liszt’s solo piano adaptation.

Leon Golub is an astrophysicist at the Center for Astrophysics in Cambridge and has been a lover of classical music for over 50 years.