Pianist Marc-Andre Hamelin performed Friday at the Strathmore. (Sim Canetty-Clarke)

Marc-Andre Hamelin is one of the smartest pianists playing today. If this description conjures up the image of a pedantic professorial type, think again: Hamelin has established himself as the thinking man’s virtuoso, and virtuosity is his main hallmark. He just employs it a lot more interestingly than most.

On Friday night at Strathmore, the exuberance with which he plunged into the classical repertory evoked something ebullient, delighted and filled with breathtaking energy, like a child plummeting into a swimming pool. He ranged over a couple of centuries of music and all over the 88 keys of the piano; the instrument, indeed, sounded a little ragged by the end of the evening, like a companion who can’t quite keep up. There was nothing childish about the smart and varied playing, though, which offered each piece — five of them, from five different musical worlds — in its own microclimate. This is how to be smart and educational about music: Simply play it with fresh interest, and very well.

Hamelin last appeared at Strathmore in 2009, as a substitute for Krystian Zimerman, so successfully that the Washington Performing Arts Society hastened to bring him back — and that he followed, to some degree, the template of that recital in this repeat appearance. At least, he followed a Haydn sonata — here, No. 34 of the composer’s oft-overlooked 62 — with Schumann, and later contrasted both with a gentle reading of Faure. The classicism of Haydn was reflected in a cut-glass approach, each note clearly delineated, crisp and shining; but the piece initially sounded as if it dated from the 20th century rather than the 18th. The notes were so thoughtfully juxtaposed that they sounded like a far more recent invention, and every phrase was considered anew — leading, at times, to a sense of continually reinventing the wheel but never merely relaxing into the easy “Haydnesque” of dancing melodies and runs.

Schumann’s “Carnaval,” by contrast, was a stormy Romantic landscape strewn with phrases that rose like boulders out of a fog of sound created by abundant use of the pedal. This is a piece of bipolar mood swings between different dance forms, tropes and characters, most notably the two sides of Schumann’s personality, which the composer named Florestan and Eusebius. Rather than simply flinging himself from one extreme to the other, Hamelin found common ground between the two personalities: Tempestuous Florestan had things in common with dreamy Eusebius’s opposite. Lyrical thoughtfulness led one to wild outbursts, the other to meditation.

The second half opened with something completely different: Stefan Wolpe’s formidable 13-minute Passacaglia, ferocious 20th-century music that bristles with tone rows (the building block of the 20th-century 12-tone technique that Schoenberg pioneered and that still sounds “too modern” to many classical listeners) and uses all of the piano to its utmost, and that, as played with Hamelin’s elasticity and musicality, was a thrilling ride. It was echoed by Liszt’s “Reminiscences de Norma,” one of that composer’s finger-tangling showpieces based on themes from the Bellini opera, but the two works were separated by the Faure piece, the sixth nocturne (op. 63), played with beautiful limpidity, like sun on water.

To demonstrate a couple of extra dimensions, Hamelin followed the scheduled program with a work of his own, the seventh of a set of 12 difficult and appealing minor-key etudes that he released as part of a CD of his compositions last year. This one, based on a Tchaikovsky song, sounded downright artless, as if Hamelin could play it with one hand tied behind his back; in fact, it was written for left hand alone and therefore far more of a technical challenge than it sounded. The second encore was Busoni’s fourth elegy, based on the tune “Greensleeves,” burning with Busoni’s typical cold alchemical flame and ending on a quirky chord that made the audience burst out laughing. It was a fine sign of the goodwill Hamelin had engendered and the degree to which he made his listeners a part of the conversation.