In the Piazza della Signoria, Florence's civic square, tourists – in their haste to admire replica statuary by the likes of Michelangelo – trample oblivious to a round memorial stone. This red-granite plaque marks the spot where Girolamo Savonarola held his bonfires of the vanities. It is also where the fundamentalist friar was hanged for heresy and himself incinerated in 1498. His remains were dumped in the Arno river, so that no relics could survive to fuel his cult.
Up the road, under Brunelleschi's magnificent cathedral dome, the austere Dominican preached powerful sermons against luxury and lewdness. His faith put him at odds with Renaissance humanism, as well as Church corruption. But as I discovered at an illuminating exhibition in Florence's Palazzo Strozzi, he was also in revolt against the values of a booming economy ruled by merchant bankers.
The Renaissance flowered in Florence alongside the birth of the modern banking system. Money and Beauty: Bankers, Botticelli and the Bonfire of the Vanities, on until 22 January, teases out the links.
Aside from its timeliness – as today's global turmoil spurs a renewed moral backlash – the show casts fresh light on Florence and its art treasures. The gallery offers a "passport" and city map flagging relevant sites (and if you collect the special stamps from five of the sites, you can obtain a free ticket to the show).
The exhibition is co-curated by the British novelist Tim Parks, who lives in Italy. Walking me through it, he told me it was "all about the tension between God and Mammon" and a crisis of irreconcilable values. The Medici bank was supreme for almost a century, until the Pope's bankers were ousted in 1494, later returning as dukes. Under Savonarola's brief republic, his Piagnoni followers (the "moaners") burnt "shameful" items – wigs and harps, perfume and chessboards, profane books and oil paintings.
The mercantile nouveau riche drove demand for such luxuries – including nudes and comely Madonnas to adorn bankers' walls.
The Palazzo Strozzi, a vast Renaissance bastion built by a rival banking family, is in the district where Florentine banking began. I strolled past designer boutiques in the Via de' Tornabuoni (Giovanni Tornabuoni was Lorenzo de Medici's uncle and the Pope's treasurer), and turned into the Via Porta Rosa, the lane where medieval money changers set up their green, cloth-covered banco – a counter for transactions.
By the late 15th century, Florence's banking empire – founded on the single currency of the day, the florin – stretched from London to Constantinople. Italy gave banking its vocabulary, from giro (bill of exchange) to bankrupt – when a banker's counter was broken.
I paused to consider present applications for the "stone of shame" in the Mercato Nuovo – a 16th-century loggia where luxuries manufactured locally from silk and English wool were sold. It's now a souvenir market where tourists pose beside a bronze boar. Half-hidden by stalls is a central flagstone resembling a cartwheel, on which miscreant bankers were chained and flogged in a punishment known as the acculattata (spanking).
There were 21 powerful guilds, from furriers to physicians, in what Dante had reviled as a city of "self-made men and fast-got gain". The Medici built their fortune in the Money Changers' Guild. On the outside of the gothic church of Orsanmichele, 14 niches house the guilds' patron saints, commissioned from artists such as Donatello (the originals are inside).
Bankers wary of inspiring envy hid their personal riches in fortress-palaces. But there were penitential ways to flaunt wealth. The bankers' chapels in the church of Santa Maria Novella have frescoed masterpieces in costly pigments, emblazoned with patrons' coats of arms. Ghirlandaio's Virgin Mary cycle, in the Tornabuoni chapel, incorporates portraits of the patron's family that scandalised the pious.
The Medici quarter, north of the cathedral, centres on San Lorenzo, rebuilt by Brunelleschi in 1425 as the family's parish church, but with an oddly unfinished façade. Lorenzo the Magnificent collected Greek texts that fuelled the classical revival. Michaelangelo – who studied drawing in the Medici sculpture gardens – designed his splendid Laurentian library in 1524, with its grey sandstone staircase and long reading room. He also built the new sacristy and sculpted some of the few tasteful items in the overblown Medici tomb complex. Here the dukes – who by now styled themselves as gods – returned for burial.
Beneath a Medici statue in the piazza, a plinth flaunts the ubiquitous family emblem – red balls on a gold crest. The heraldic balls also identify the Palazzo Medici (later Riccardi), begun in 1444. Its hidden gem is a tiny chapel with Benozzo Gozzoli's jewel-coloured frescos of the Procession of the Magi through a Tuscan landscape. The portraits of Medici on horseback allude not only to the Bible's merchant-kings, but to the Company of the Magi, a quasi-political brotherhood whose pageants paraded Medici power through the streets.
Just north is San Marco, the Dominican monastery revamped by Cosimo the Elder (who used it as a retreat), with frescos by Fra Angelico. It's now a museum. Even the cramped novices' cells upstairs have stunning devotional frescos. Savonarola, who was prior in the 1490s, was arrested here to face trial, then worshipped as a martyr. His inky cloak survives in a glass case.
After admiring more Botticellis in the Uffizi – painted for his Medici patrons – I repaired to the gallery's Bartolini café, for a glass of prosecco on the terrace and views across the Piazza della Signoria.
At sunset, I crossed the Ponte Vecchio, as the bridge's jewellers were closing shop, to dine at Il Santo Bevitore on Via Santo Spirito, one of six restaurants with special menus to chime with the Strozzi palace show. The sybaritic confections used truffle oil and edible gold. Savonarola's moaners would not have approved.
Travel essentials: Florence
* Florence is served by CityJet (0871 66 33 777; cityjet.com) from London City and Meridiana (0871 423 3711; meridiana.it) from Gatwick. Pisa airport has many more links from the UK, and offers frequent direct bus and rail connections to Florence
* Money and Beauty is at the Palazzo Strozzi (00 39 055 264 5155; palazzostrozzi.org) until 22 January. Open 9am-8pm daily (Thursdays to 11pm), admission €10.
* Palazzo Medici-Riccardi (00 39 055 2760; palazzo-medici.it). Open 9am-7pm daily except Tuesday, admission €7.
* Italian State Tourist Board: 020-7408 1254; italiantouristboard.co.uk