Re: Maths
Clinton's administration briefly balanced the yearly budget, yes, but... honestly, people make a much bigger deal out of that than it really was. Don't get me wrong: I voted for Clinton, I campaigned for Clinton, I was (on balance) happy with Clinton's presidency... but from a bird's-eye view of his entire term in office, the balanced budget was ultimately the least meaningful thing they did. (Not to say that it was bad, it was just pointless. They did plenty of other, more meaningful bad things: DADT, DOMA, the 1994 "tough on crime" bill — there were some real stinkers in there, for sure.)
For starters, there was already plenty of outstanding debt accrued, so it amounted to little more than a temporary pause in the growth of that debt. The debt itself was not meaningfully reduced even when the budget was balanced, so there's an aircraft-hangar-sized room for debate about whether there's any necessity for, or even benefit to, having a balanced budget or a budget surplus if it does nothing to reduce the debt.
(When people talk about eliminating the deficit (the imbalance in the budget), they often mistakenly conflate it with eliminating the debt itself. Which... is not only incorrect, it's an economic impossibility. Just as a practical matter, there isn't enough currency in the entire world to cash out the full $39 trillion and change the US theoretically "owes" as its national "debt". To repay all of its creditors in physical currency, step one for the US would have to be instructing the Mint to start printing the cash required to do it. Which would, of course, so completely devalue the US dollar that it would be rendered worthless.)
Most people "know", conceptually, that national debt for a country has almost no resemblance to the personal credit card debt they carry. Nevertheless, most of us still fall back into patterns of thinking about it in exactly those terms, when we do think about it.
National "debt" is more akin to selling shares in the country. As long as the nation is stable and relatively functional (so, you know... we're admittedly not at our best there, currently...) ...As long as we're still a nominal superpower, creditors aren't particularly interested in recovering their investment principal. They're much happier profiting off the interest it generates, effectively using the country as a savings account for their wealth.
The US has had a national debt ever since its inception. (Revolutions are expensive! We started $75 million in the hole. ...These are unadjusted numbers, BTW, so that's $75 million in 1790 money.) The debt fluctuated up and down a bit in the $70 million - $105 million range through around 1825, then a concerted effort was begun to reduce the balance. In 1835 it hit an all-time low of $34 thousand 1835 dollars. By 1840 it was back up to $3.5 million, and by the end of the Civil War it was measured in the billions. It has broadly trended upwards ever since. There were occasional, small dips (1946: $270M; 1947: $258M; 1948: $253M // 1956: $273M; 1957: $270.5M), but nothing meaningful. Even during the Clinton "balanced budget" years, the debt actually increased (because interest on the debt still accrued) in raw-dollar terms — but the amounts were so small, the slope would reverse if you adjusted for inflation.
It's also worth noting that those brief actual-value reductions in the outstanding debt occurred — I would claim, not coincidentally — during periods when the top income tax bracket (the tax on the wealthiest Americans' highest earnings) was over 90%. Radical tax "reforms" (AKA pandering to the rich) begun in 1964 chopped the rate down from 77% that year to just ~39% in 1987, which is where it's hovered ever since. And the debt, again not coincidentally, has steadily marched upward. (Though some extraordinary spending events, like the COVID-19 response and subsequent financial stimulus, goosed it extra hard.)
(As a final note, I am not an economist and it's probably safest to assume that everything I've just written is incorrect. I'm certainly not going to blindly trust me!)