The third president of the United States was a lifelong admirer of W. A. Mozart. Or rather, of Mozart's music; he arranged to meet Mozart in Paris when he was Minister to France (August 1784–September 1789)—purportedly with the intention of commissioning a work in honor of his wife—but was so disenamored with the man's demeanor in person that he dropped these plans. Jefferson was still able to separate his appreciation of the music from the man: long after this unpleasant meeting, Jefferson would write of Mozart's "heavenly music".
I've been reading some of Jefferson's writing on music theory, and given his perspective and his love for Mozart's music, I think the Symphony No. 40, KV. 550 would be so astounding to him—particularly in its use of modulation—that he would have had to write about it if he'd heard it—but the contemporaneous naming conventions (or lack thereof) make it difficult to search online archives of his writing for such mention. I feel as if this gap could itself constitute circumstantial evidence he never read the music or heard the work performed.
But absence of evidence is not evidence for the absence, so I've been trying to research the question.
Exactly when the work was first performed anywhere is subject to great dispute; it's reasonably attested to have been composed in 1788, and had concert revisions in 1791, so one can probably assume it was first performed some time within that period. In fact, there's good reason to believe its first Vienna performance was in 1791, conducted by Antonio Salieri. (It's sometimes been asserted that Mozart never heard his symphony performed, but this appears to be aprocryphal.)
In any case, it seems that Jefferson almost certainly could not have heard the work performed in concert while he was in Europe. But could he have ever heard it in America?
As far as I can find, there were no standing symphony orchestras in the United States until the 1840's (long after Jefferson's death in 1826), but there were chamber orchestras and orchestras performing opera in the two decades bookending the 18th and 19th Centuries. (In 1803, with the Louisiana Purchase, the country acquired at least two orchestras already operating in New Orleans, including the opera Théâtre St. Philippe. But President Jefferson never visited New Orleans, or anywhere in the Louisiana Purchase as far as I can tell.)
I can find references to symphonic works being performed in America in the time period between Jefferson's inauguration and his death, but I haven't found any mentioning Mozart specifically until the 1830's, and none specifically mentioning this particular piece until 1850 (when it was performed in Boston).
Concerts in New York, Boston, Philadelphia and Charleston in the 1840's–1860's each are claimed to be the first to perform the work in their respective cities. If that is true, since all four were after Jefferson's death, it seems unlikely that Jefferson ever heard this piece in symphonic form.
(But perhaps he heard it in the form of a reduced arrangement, maybe even played on one of his several keyboard instruments he kept at Monticello or at one of the chamber recitals he arranged at the White House or at Monticello.)
I'm curious if anyone else knows of any historical evidence one way or the other.