Actually, it's from his Symphony No. 9, better known as the Symphony from the New World, and it occurred to me that this would be a good occasion to lay out my
Haydn: In the 18th century, music was considered a disposable art, and composers did not number their symphonies, as nobody was expected to collect them all. Accordingly, the numbers we use today were applied retrospectively by somebody else. Haydn's symphonies were numbered in the early 20th century by a scholar named Mandyczewski. He did a pretty good job. He omitted any misattributed works and caught all but two genuine extant works. (Those two, early and obscure works, are now known as Symphonies A and B.) And, although there are a few chronological clangers in his list, he got them mostly in a roughly accurate order of composition. Accordingly, Mandyczewski's list of 104 Haydn symphonies may be, and is, used with confidence.
Mozart: Much more of a headache. The standard list of 41 Mozart symphonies was compiled in the early 19th century by a publisher that wasn't paying much attention. Though the chronology was accurate, due to Mozart's habit of dating his scores, the list included a few works that Mozart didn't compose, but only had manuscript copies that he'd written out (this is why you never hear anything of a No. 37), and it omitted almost as many early works as it included, minding the additional problem that, with Mozart, it's sometimes hard to tell what counts as a symphony and what doesn't. The fuzziness, however, is mostly with juvenilia: mature Mozart, the 15 or so symphonies from No. 25 on up, is a stable body of work. But the list of 41 has no authority (and if anybody ever says, "Mozart wrote 41 symphonies," that's a sure sign they know nothing about Mozart), and to be a member in good standing of the effete corps of Mozartean snobs, you will refer to his symphonies, not by those numbers, but by their Köchel numbers, those being the equivalent of opus numbers, the serial numbers from a scholar's catalog of all of Mozart's works. By this, for instance, the "Jupiter" Symphony is not Symphony No. 41, but K. 551.
Lesser 18th century composers are even more of a mess than Mozart, so be thankful that you don't have to read me trying to explain those.
Beethoven: The first major composer to number his symphonies himself. Nine, in chronological order. No problems.
Schubert: Did not number his, but the problems are not of his making. He wrote six early symphonies easily numbered in chronological order. After that it becomes difficult. The standard list continues with, in chronological order: No. 7, incomplete, a full-length sketch in E Major without orchestration; No. 8, also incomplete, a torso of two fully-orchestrated movements in B Minor, followed by sketches for a third but no fourth; and No. 9, the Great C Major Symphony, the only other fully complete symphony he wrote. No. 7 you are unlikely to come across, while No. 8 is the famous "Unfinished" Symphony. The problem is that some scholars don't think No. 7 belongs on the list. (There are also some other incomplete sketches that aren't on it.) They deal with this in one of two ways: 1) by kicking the other two down a notch, making the Unfinished No. 7 and the Great C Major No. 8; 2) by leaving the Unfinished at No. 8 and folding the Great C Major in as No. 7, even though it was written afterwards. Accordingly, the Great C Major may be No. 7, No. 8, or No. 9, on different lists. Just to make things more complicated, a reconstructed version of a set of sketches that postdate the Great C Major are sometimes listed as Symphony No. 10.
Mendelssohn: Wrote two sets of symphonies. His juvenile symphonies or string symphonies, usually so referred to, number twelve or thirteen, depending on whether one counts an incomplete movement. His mature symphonies number five, but they're not in the order of composition but of publication. Mendelssohn only published three of them: No. 1, a light piece in C Minor; No. 2, "Lobgesang", which is really an oratorio rather than a symphony; and No. 3, the "Scotch" or "Scottish". He withheld No. 4, the "Italian", because he wanted to revise it (but never finished doing so), and No. 5, the "Reformation", because he thought it sucked, a judgment with which I cannot entirely disagree. Those two were published with those numbers after his death, but the symphonies were written in the order 1, 5, 4, 2, 3.
Schumann: On the surface, a simple canon of four symphonies, but it's more complicated than that. No. 4 was actually written contemporaneously with No. 1, but, like Mendelssohn with his "Italian", Schumann withheld it for revision. Unlike Mendelssohn, he did get around to finishing it, but only after he wrote No. 3, so he called it No. 4. So there's two versions of that one floating around. There's also an early incomplete work known as the "Zwickau" Symphony, for where he lived when he wrote it, and another piece he wrote at the same time as No. 1 and No. 4 that he called "Overture, Scherzo, and Finale". It's a symphony without a slow movement, and many Schumannophiles count it as one.
Bruckner: Not much of a numbering problem, except for the amusement value of an early work he considered not up to snuff as a numbered symphony and called "Die Nullte" or No. 0. There's also a student work predating that sometimes called No. 00 (but not by the composer). No, the problem with Bruckner is the multiple versions of his symphonies, but that's another matter.
Brahms: Four symphonies. No problems.
Tchaikovsky: On the surface, six symphonies. But there are a couple of catches. First is that he also wrote a work called the "Manfred" Symphony which he published but, for some reason, didn't number. It comes between No. 4 and No. 5. Second, between No. 5 and No. 6 he sketched out in full a symphony he abandoned and reworked into a piano concerto. (Not the Tchaikovsky piano concerto, which is No. 1; this one is No. 3.) It's been reconstructed as a symphony and called No. 7, as the lowest available number, but it's rarely played.
Dvorak: A real headache, but only if you use old sources. Dvorak wrote four early symphonies he never published; indeed, the score for one was lost and not found again until decades after his death. Then he wrote five more which he did publish, but he numbered them in the order of publication, not the order he wrote them in. Around the 1960s it became customary to resurrect the unpublished four and renumber all of them in the order he wrote them. So on current lists you'll see him as the author of nine. The catch is those older sources, which are sometimes not easily identifiable as such. But, as each successive Dvorak symphony is more popular than the one before, on a very steep curve, if you see a casual reference to No. 2, No. 4, or No. 5, chances are they mean the works you know as No. 7, No. 8, or No. 9, respectively. (No. 9 alias No. 5 is the famous Symphony from the New World.) But ... No. 7 is alias No. 2, you say? How did that happen? Order of publication vs. order of writing.
Mahler: No numbering problems, but this does give me the opportunity to tell about Mahler's paranoia over the Curse of the Ninth Symphony. Both Bruckner (Mahler's mentor) and the great Beethoven died during or soon after writing their Ninth Symphonies, and Mahler was obsessed with fear that he'd do the same. So when he wrote his vocal ninth, he didn't number it, and just titled it Das Lied von der Erde instead. Then he wrote a purely orchestral work and called it No. 9, and figured he had cheated Death. Silly Mahler! He should have remembered Bruckner's "Die Nullte" and figured out that the curse isn't about how many symphonies you actually write, but what numbers you give them, because soon afterwards, while working on No. 10, he died, at an early age.
Vaughan Williams: Nine symphonies, now straightforwardly numbered, but it didn't start out that way. His early symphonies were either descriptive works with titles or abstract works identified only by key. It was only when he published one that he called Symphony No. 8 that the numbers retroactively dropped on its predecessors, and they've been used ever since. Fortunately in this case there was no ambiguity; there is a minor 19th century composer whose Symphony No. 2 leaves unresolved which of two earlier unnumbered works he considered to be Symphony No. 1.
Prokofiev: Seven symphonies. No. 1 is the famous Classical Symphony and was only numbered in retrospect; the number isn't always used. No. 4 exists in two versions, the revised one coming just after No. 6.
Copland: The only Copland symphony regularly heard is No. 3, the last one, which is the only one without any numbering footnotes. A work usually called the Short Symphony is No. 2. The Symphony for Organ and Orchestra is No. 1, but that number only properly applies to a revised version without the organ. There's also an unnumbered Dance Symphony.
Shostakovich: Fifteen symphonies. The only thing you need to know is that some works performed under the titles Chamber Symphony or Symphony for Strings were not Shostakovich's idea, but are arrangements for orchestra by the conductor Rudolf Barshai of some of Shostakovich's string quartets.
Anybody else, either no numbering problems (some composers didn't number their symphonies at all, like Berlioz or Liszt or Stravinsky or Britten) or I'm arbitrarily declaring them not that major.