The Beatles in general, and Paul in particular.

In the 1960s music in the classical tradition had moved so far away from popular music, it had become unapproachable to the average person. Meanwhile, technology was advancing, both in the studio and in performance, so you see the Avant-garde starting. And at the same time popular music had suddenly become a huge industry, mainly aimed at the boomer generation, the largest ever, who had disposable income.

The Beatles brought all of that together in one act.

- They took inspiration from music in the classical tradition, often finding influence in Mozart or Bach, for example.

- They also had an interest in the Avant-garde, becoming pioneers in tape loops and world music.

- And, of course, they had the knack for writing extremely successful popular music. Paul McCartney has an ear for melody that you would have to go back to Bach or Mozart to find a better melodist.

They changed how music is recorded (see Abbey Road studios, etc), they changed how music is packaged (see Sgt, Pepper), they changed how music is marketed (see how they pioneered music videos), but most importantly, they changed how we perceive music. Before the Beatles, popular music was just for fun, not taken seriously. But the Beatles changed that. Suddenly Leonard Bernstein is talking about their music, professors are using Sgt. Pepper in the classroom when it came out, and Cambridge includes a guide to their oeuvre.

Other artists have claims to history, but no one artist brings together both peak popularity and critical acclaim at the level the Beatles have.

If all they had ever done was All You Need is Love live for the One World broadcast, they would still be in the history books, having played to an audience of about 700 million people, but they also have 132 weeks at the top of the album charts from a career that lasted 7 years (Taylor has 98 weeks over 20 years), 20 number 1 singles (27 if you count England), etc.