I’m sorry to remind you of this, but the year 1995 — and the release of alt-rock stars The Smashing Pumpkins’ diamond-certified double album, “Mellon Collie and the Infinite Sadness” — was 31 years ago.

The upside to that “we’re all getting old” feeling is that the band is celebrating more than three decades of the album that cemented their place in rock history with their The Rats In A Cage Tour, named for a lyric from the album’s hit track “Bullet With Butterfly Wings.”

The three intervening decades since the release of “Mellon Collie,” their third studio album, have been tumultuous for the band, but they have continued to steadily release music in the past decade and a half. They’ve also visited Pittsburgh plenty, most recently playing with fellow ’90s alt radio veterans Green Day at PNC Park in 2024.

At their Tuesday night show at PPG Paints Arena, the band set out on an ambitious double set, first performing about half of the songs from “Mellon Collie” and then bringing out another 75 minutes of deep cuts and fan favorites from throughout their discography.

They kicked off in maybe the most surprising way possible, with their two biggest hits back-to-back. In comparison to many of their heavy songs, “1979” — their highest-charting tune — was pretty quiet and poignant, but it also makes sense as the opener for a tour that is essentially celebrating nostalgia.

In contrast, the second song was “Bullet With Butterfly Wings,” a barely restrained rocker that found lead singer Billy Corgan straining his unique voice with rage-filled screams towards its end.

In total, Tuesday night’s crowd got to hear 16 of the original album’s 28 songs in that first set. They included deep cuts like the dreamy and expansive “Porcelina of the Vast Oceans,” which ebbed and flowed for almost 10 minutes under blue-green lights, and “By Starlight,” which made Corgan’s occasionally grating voice pretty and lilting while thousands of cell phone flashlights twinkled to life.

Corgan paused to thank everyone for coming out, and then said, “Time to tell some jokes. Where does a penguin keep his money? In a snow bank.”

After playing the airy, mid-tempo “Galapogos,” he paused to say, “I forgot when I told that joke that the Penguins play here, so I mean no disrespect. I’ve got more dad jokes if you want them.”

In the midst of the set, they brought out another of their “Mellon Collie” hits, “Tonight, Tonight.” Everything about the song felt sweeping and epic, from the rolling drums to the urgent guitar and Corgan’s gliding voice. They also played “Zero,” a dark and guitar-driven tune that embodies the emotions that Corgan said the record was written to express.

“The album dealt with alienation and disassociation and depression and rage,” he explained.

They wrapped up the first set with the instrumental title track to the album, then went off as the stage was reconfigured.

The second set was packed with deep cuts, starting with the plodding and lengthy “Sojourner,” which felt spacey and vibey under purple-blue lights. There were 14 songs in total, pulling highlights like “Edin” and “War Dreams of Itself” from their 2024 release “Aghori Mhori Mei.”

Another highlight was incendiary “As Rome Burns,” which had the whole band playing at the top of their game but especially showed off the skills of drummer Jimmy Chamberlin.

There were hits in that second half, too. Corgan sounded plaintive through the sincere tune “Disarm,” maybe his best vocal performance of the night. They followed that with the industrial, wonky “Ava Adore” with pulsing red lights. Then there was “Today,” the cheerful, bright tune that got the audience singing loud enough to be heard over the deafening guitar, and finally “Cherub Rock,” which made the fans even louder as they shouted “Let me out” over and over.

They finished riding the marathon-long roller coaster of the setlist with quiet, contemplative “Jesus is the Sun,” then thrasher “The Everlasting Gaze” and finally the full-on instrumental jam “Superchrist,” with all of the band members flaunting their talents in cheer-inducing solos.

After 31 years, 30 songs and nearly three hours, The Smashing Pumpkins still seemed to be having a great time — despite the depressing album that sparked this tour.