Nashville. Capital of Tennessee. Seat of Davidson County, whatever that is. On the Cumberland River, wherever that is. Population, 635,000, which last week became 635,001.

A census would have added Jake Gyllenhaal.

Saturday, I read a pop/celebrity magazine with stories about Taylor Swift, 21, and “older man” Gyllenhaal, 30. Page 42 said: “Hot Stuff. That was fast! Taylor Swift’s romance with Jake Gyllenhaal is already cooling off.” The front cover blared the headline: “Taylor Swift burned by Jake.”

If she were burned by Jake, it would have had to be in her own kitchen. He’s been with her in her hometown as recently as last week. She lives in Nashville. He does not. Wednesday night, they were together in its local eatery Boundary. Where he slept, couldn’t tell you. Maybe he booked a hotel room under the name “Hot Stuff.” Friday, both went to the airport and were cosseted in a high-security area.

Trust me, Miss Swift is not checking into any burn unit.

WILL Smith producing “Annie” for the big screen. And saving money. Daughter Willow‘s got the lead. Jay-Z will do the oom-pah-pah . . . Sacha Baron Cohen to star in “The Dictator,” based on a novel by Saddam . . . Harvey Fierstein to do B’way’s “Kinky Boots.” The workshop’s in May.

BURT REYNOLDS walking Park Ave nue. No lady with him. Just his cigar . . . Brits call Ricky Gervais “cheeky chappie” . . . A restaurant you must visit is Trattoria Dell’Arte, Seventh between 56th and 57th. So popular that it’s hard to get in. But wonderful. And try their thin pizza . . . Yesterday you may have read that Newsweek will go jazzier. Weeks ago. Weeks ago. Like weeks ago, I told you that.

SUNDANCE had thrills this week. Be sides R. Redford, R. Kennedy Jr. stopped by to use the fax machine . . . Of big-time movie events, worst film ever is . . . “No Strings Attached.” Natalie Portman and Ashton Kindergarten. So cheesy, its producer must be named Kraft. Friends left when Ashton showed his bare rump and clutched his front bump. Those naked parts may do something for Demi Moore, but they did nothing for us. It was disgusting.

AND my gratitude for wacko nutso bike commissioner Janette Sadik- Khan turning this great city into a bicycle lane. Next it’s perambulators on Fifth Avenue. This wacko nutso bike commissioner about whom nobody ever heard before comes to work on a two-wheeler. The other day, crossing side street on Park, I, as always, looked right. While I looked right, a bicyclist sideswiped me whizzing from the left.

ROSIE Perez‘s so-far-untitled Random House memoir will tell how she got Peter Weir‘s film “Fearless” with Jeff Bridges, Isabella Rossellini, Benicio del Toro. He asked why she, a Catholic, crossed herself oddly. She said: “I’m exhausted from 25 cups of morning coffee, which had me racing to the john.” So when he asked her to lie on the floor, she fell asleep.

About her lone Oscar party at a Mexican barbecue. “I wore overalls and a tee. Getting out of the car, they ordered me to the kitchen. I stayed and ate crab cakes with the staff all night. When they told me to go to the Oscar party, I said, ‘Eff them.’ And I piled all their bottles of Champagne into my car.”

THE British geology department sent me pages about Queen Kate Middleton. Saying her lineage is Jewish. Stewardess mother, Carole Goldsmith. Grandparent Ronald James Goldsmith, a lorry driver. Great-grandparent Stephen Goldsmith, a laborer. Harking to 1851, there’s John Goldsmith, a bricklayer.

ONE thing I don’t understand about football. Every team has voluptuous cheerleaders — yet every time the team scores, the players hug and pat one another on the behind.

SO we’re electing a president. In 1920, Warren Harding defeated Democrat James Cox on Nov. 2. His victory’s the largest popular vote percentage-margin in US history. Called “The Ohio Gang,” his Cabinet members were then tried, convicted and jailed for bribery and fraud . . . May the best man win.

BEN’s restaurant features an ethnic show every Saturday, except when not enough people come to fill it . . . But filled nightly is Bette Midler‘s New Leaf eatery in the Cloisters. Stunning. Handsome staff, food excellent. Please go . . . Ernie Anastos, en route to Fox, jumped over snow piles to get out of his car on East 68th . . . Make sure you see the Natural History Museum’s special on the brain. Took 2½ years to complete and it’s astounding. With what happened to our Tucson congresswoman, everyone’s checking with the museum on how the brain operates.

IN 1984, John Catsimatidis, who owns groceries like Red Apple, Gristedes, was approached to buy Snapple, which now makes more money than China. The asking price then was $30 mil. Said John: “No. What do I want this sh – – for?”

Only in New York, kids, only in New York.