ON THE STEPS of the Smith County Courthouse in Carthage, Tenn., came the official announcement from Sen. Albert Gore Jr. that he is running for the Democratic nomination for president. This is hallowed Democratic ground, two counties over from Andrew Jackson's Hermitage, the home town of Cordell Hull and of Mr. Gore's father, who was first elected to the House 49 years ago and stood by his son's side yesterday.

Albert Gore Jr. is the first Vietnam veteran formally announced in the Democratic race (Alexander Haig is the first in the Republican race); born in 1948, he is the first official candidate who is undeniably a baby boomer; coming from Tennessee, he is also the first announced Democrat from the South. Yet he doesn't fit precisely into any of these pigeonholes. He is not one of those Vietnam veterans who find fault with all things military (he's for the MX missile, for example); he has criticized rather than quoted rock lyrics (his wife wrote of "How to Raise PG Kids in an X-Rated Society"); his insistence that he is "a national candidate from the South" is supported by a voting record close to most northern Democrats'.

For many voters a candidate 40 years old, even with 12 years in Congress, has a special burden of proof. Mr. Gore cannot expect to succeed unless he proves he is superior in intellect and in leadership ability to his rivals. He has been elected by impressive margins in Tennessee, and not just because of lingering affection for his father, the longtime senator and governor. On the difficult and central issue of arms control, he made himself a national leader while a junior member of the House by close personal study and original and persuasive proposals. He's the author of a national organ transplant act, and has taken the lead on protecting the ozone layer.

Some argue these are just motherhood issues, and that Mr. Gore avoids making enemies. But there's a case for leadership that focuses not on familiar issues that are divisive but on unfamiliar issues on which consensus is needed and possible. Mr. Gore calls himself a "raging moderate."

There is a hint of hurried opportunism in the Gore candidacy. At first he declined to run; then Dale Bumpers and Sam Nunn bowed out, making the contest more attractive to him in the dozen southern states choosing delegates on Super Tuesday; then Mr. Gore made a favorable impression on a group of fund raisers headed by Nathan Landow; shortly afterward he announced he'd announce. Now he has. His task as a candidate is to distinguish himself from and elevate himself above a pack of candidates who, even to attentive Democrats in Iowa and New Hampshire, tend to look interchangeable.