The Last Night of the Proms is always a beautifully choreographed event, and this year’s was no exception. The format changes little, but each year a new selection of works is chosen to fill the slots. The BBC Symphony Orchestra, always the backbone of the season, somehow manages to sound fresh for their final outing.

The Vienna Philharmonic makes a beautiful sound, no question about that: the question is what to do with it. Michael Tilson Thomas has some ideas, but they are mostly low-key. He is currently touring with the orchestra, and seems to have been chosen as a safe pair of hands, offering elegant and lyrical interpretations, but without any extravagance.

Outlines of a real face had begun to emerge in Daniel Harding’s conducting personality. His youthful rise to the top initially yielded neutral concerts with the LSO and a glassy, overpraised recording of Mahler’s Tenth in the Deryck Cooke completion with the Vienna Philharmonic. But then I heard a supple, intensely lyrical Brahms Third in the Concertgebouw and what came across on CD as a fine live interpretation of Mahler Six from Munich.

Amazingly, last night Sir András Schiff scored a Proms first with his performance of Book One of Bach’s The Well-Tempered Clavier. Never before has even half of the sublime and seminal “48” taken the Royal Albert Hall stage in unmutilated form. The WTC could have found no better advocate.

It can’t be too long before “women” no longer needs to prefix “conductors” to define what’s still a rare breed. Yet seven at the Proms is certainly an improvement, with many more coming up through the ranks. And American Karina Canellakis turned out to be very much the season’s final trump card.

Even tuning up, the multinational musicians of the Freiburg Baroque Orchestra make a lovely sound, well-anchored by the tug of four period-instrument cellos and three basses, yet buoyant and stippled with upper-wind colours, flutes circling and dipping like a cliff-edge bird colony. Ideal, then, for the Hebrides Overture which opened this Mendelssohn matinee (★★★★).

How do you get to heaven, especially if you need to reach the pearly gates by way of the earthbound acoustics of the Royal Albert Hall? With Chief Conductor Daniele Gatti as their spirit guide, the sumptuously arrayed pilgrim band of the Royal Concertbegouw Orchestra from Amsterdam sought different routes in the centrepieces of their pair of Proms.

No-one, least of all the players, will forget Semyon Bychkov’s 2009 Proms appearance with the BBC Symphony Orchestra in a poleaxing interpretation of Shostakovich’s Eleventh Symphony.

No sunshine without shadows was one possible theme rippling through this diva sandwich of a Prom. Even Richard Strauss's chaste nymph Daphne, achieving longed-for metamorphosis as a tree, finds darkness among the roots; and though Renée "The Beautiful Voice" Fleming has a heliotropic tendency in her refulgent upper register, her mezzo-ish colours are strong, too.

If individual greatness is to be found in the way an artist begins and ends a phrase, or finds magical transitions both within and between pieces, then Pavel Kolesnikov is already up there with the top pianists. Listeners tuning in midway through the peaks of his lunchtime Prom – the great Chopin Fantaisie or the Fourth Scherzo – might have thought they were listening to an old master, while what we saw was a modest 28-year-old who looks much younger, but who moves with total assurance and absence of flash. His performance of Tchaikovsky's massive Second Piano Concerto with the National Youth Orchestra of Scotland was one of the highlights of last year's Proms; this took us even further in a Chopin odyssey intelligently planned and ineffably well-executed.

Kolesnikov programmed his recital in the shape of a giant Chopin butterfly with two iridescent wings of consecutively played miniature masterpieces leading to bigger numbers and the great Op. 49 Fantaisie as the central body. Its imaginative genius for connection is something I well remember in a Chopin recital by his great mentor, Elisabeth Leonskaja, each of her halves played without applause between pieces; Kolesnikov already has a similar balance between Russian orchestral pianism and the capacity for sudden flight. The concert began with spaciousness in the A flat major Waltz, but no repeat is ever the same in this pianist’s hands, and nothing stays solid for long. Extremes were licensed in the C sharp minor Waltz, beautifully connected to the Fantasie-Impromptu in the same key. Kolesnikov never rushes: even his most headlong brilliance comes up for air in well-placed "breaths".

Five of the amazing Mazurkas, a selection of which Kolesnikov has recorded, showed Chopin’s infinite variety on the most intimate scale: playful in the major-key specimens, from the charm of the composer’s youth to the contrast of the rustic-rollicking C major, Op. 56 No. 2 with the sophisticated A flat major, Op. 50 No. 2; and introspective in the minor, supremely so in an intensely chromatic swansong (Op. 68 No. 4). Kolesnikov had even chosen a brighter action to his Yamaha plano for the third part of his programme, necessitating a keyboard change by four technicians while he chatted sensibly with Petroc Trelawny; like Richter, he never makes the instrument produce the brittle clarity for which it can be notorious.

Those mazurka rhythms made an immediate connection with the start of the E major Scherzo (Chopin's manuscript pictured above), a paradigm of Kolesnikov’s sleight-of-hand between the well-weighted and the ethereal. And the Fantaisie showed his integrity in large-scale thinking, feeling very much like a final work – though in fact it was composed eight years before Chopin’s untimely death – in its search for a peace found in the very moving benediction before the still-questioning final bars.

The bright encore was the Grande Valse Brillante, scaled down at first to intimacy but growing wings like everything else in the programme. The BBC’s Young Generation Artists, including Kolesnikov among their number, are no chrysalids when they make their first radio appearances, but when they take off into the big wide world like Francesco Piemontesi and his equally thoughtful confrère whom we heard here with such unremitting pleasure, the choice is fully vindicated. Besides, anyone who relishes the risk-taking of Amy Winehouse, stands in the Arena for the Proms late-nighter of Rachmaninov's Vespers, and collects old perfumes, is fine by me.

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Next page: watch Kolesnikov play Chopin's Mazurka in A minor, Op. 68 No. 2