EXETER, N.H. -- When Paul Simon, the senator from Illinois and Democratic presidential contender, visited the public high school here several weeks ago, he was in his element. Speaking under a banner that hailed the school's winning the New Hampshire ''academic decathlon'' in 1985 and 1987, the scholarly candidate (author of 11 books) spoke as earnestly to the students about the importance of their learning foreign languages as he did about his own campaign.
One of the few adults who had dropped in to hear the speech was deeply impressed. ''It's so refreshing to hear a candidate who is not totally preoccupied with his own ambitions,'' said the woman, who declined to give her name because, she said, ''I'm a Republican looking around for someone to support.'' When do you think you will find him? she was asked. ''I think,'' she replied, ''I just did.''
The conversion in Exeter was a tiny part of what may be the biggest story in presidential politics at the moment. It is the emergence of the unglamorous, still largely unknown Simon, a first-term senator of 58, as a serious contender for the Democratic nomination.
Simon wasn't planning to run this year; he was the chief Capitol Hill backer of his friend and fellow liberal, Sen. Dale Bumpers of Arkansas, until Bumpers unexpectedly balked at entering the race. Without waiting to assemble an organization or campaign bankroll, Simon announced on May 18, saying: ''I stand here as a Democrat who is not running away from the Democratic tradition, not a neo-anything.''
Artfully capitalizing on his hickish, odd-duck appearance while suggesting he was not one of those ''slickly packaged'' politicians, Simon said: ''To become fashionable, some people tell me to get rid of my bow tie and my horn-rimmed glasses. Well, Harry Truman wore a bow tie and horn-rimmed glasses, and he didn't knuckle under.''
''He's one of the best politicians Illinois has seen,'' state Republican chairman Don Adams told me the other day. ''And I emphasize, he is a 'politician.' He likes to stand above the other politicians, like Jimmy Carter did, as if he wouldn't create an image like they do. But it's all image -- starting with the bow tie.''
Adopting Truman as a role model was just the beginning of Simon's shrewdness. ''He's hot,'' said Republican Edward J. Rollins, manager of Ronald Reagan's 1984 campaign, ''because he was the first to recognize that with Kennedy and Cuomo out, there was a populist void . . . no one really out there delivering the liberal message except Jackson.''
The Illinois senator has moved into the top tier of candidates in Iowa and has planted his flag as an alternative to the favored Dukakis in New Hampshire. The southern superprimary is a big hurdle for him, but if Jackson takes the play away from all the white candidates there, then the action moves back to Illinois, New York and Pennsylvania -- where Simon could be as strong as anyone.
Simon thinks his unabashed belief in activist government is part of his appeal. But a larger part, he told me last August when he was barely a blip on the screen, is that ''people want somebody who believes something and has a sense of direction.'' Pollster Paul Maslin, one of his main strategists, says: ''People can see that Paul is real, he's solid and he's rooted. For different reasons, he and Jesse Jackson are creating the most personal response out there. . . . They are willing to speak their beliefs.''
Simon's beliefs are a bit of a hodgepodge. Alone among the 1988 candidates, he voted against all the tax cutting of the Reagan years and still asserts it was wrong. Not even Jackson is matching Simon's proposal to make the federal government the employer of last resort for all long-term layoff victims. And no one else has echoed his promise to have a plan for financing long-term health care costs ready within 60 days of taking office.
At the same time, Simon supports the balanced-budget amendment and promises to end deficits within three years. How he would manage all this is a mystery. In Dover, N.H., he talked of financing his unformulated long-term health care plan by higher Social Security taxes, sin taxes or unspecified ''changes in inheritance taxes.'' A short helicopter ride later, here in Exeter, he said he would end deficits by: cutting spending ''particularly in the area of defense,'' by stimulating the economy with his public-employment scheme, and ''only as a last resort would I increase taxes, and I don't believe that will be necessary.''
As his stock soars, rivals are sure to question Simon's budgetary math and thereby chip away at his political credibility. But his history shows him a tough man to pin down -- or knock down. In the 1984 Senate campaign, incumbent Republican Charles H. Percy's ads assailed Simon as a man ''addicted to taxes'' and tried to dramatize the ''startling'' difference between Simon's liberal House voting record and his independent-sounding stump speeches.
But Simon prevailed by getting one of every six Reagan voters to split his or her ticket, running even with Percy among moderates and independents. ''Never underestimate him,'' Republican chairman Adams advises.