What songwriter has penned the most number one hits worldwide?

Most no. 1 hits ever by an artist:
Paul McCartney is credited as the writer on a total of 32 number one hits in the US and 28 in the UK (Co-Written). More than any other artist; even Elvis Presley.

https://en.wikipedia.org/wiki/Paul_McCartney

Diane Warren

To date she has had over 80 songs charted in the top 10. Diane Warren has written for such legends of song as Elton John, Tina Turner, Barbra Streisand, Aretha Franklin, Roberta Flack and Roy Orbison. Recently, artists such as Patti LaBelle, 'N Sync, Gloria Estefan, Britney Spears, Christina Aguilera, Reba McEntire, Whitney Houston, Enrique Iglesias, Aerosmith, Ricky Martin, Faith Hill, Celine Dion, Mary J. Blige and LeAnn Rimes.

https://www.songhall.org/profile/Diane_Warren

Most Number Ones

By Writer

Paul McCartney 31
John Lennon 25
Barry Gibb 16
Brian Holland 15
Lamont Dozier 15
Robin Gibb 13
Eddie Holland 13
Maurice Gibb 11
Carole King 9
Lionel Richie 9
Gerry Goffin 8
Mick Jagger 8
Keith Richard 8
Jeff Barry 7
Daryl Hall 7
Michael Jackson 7
Bernie Taupin 7
Stevie Wonder 7
Burt Bacharach 6
Harry Wayne Casey 6
Richard Finch 6
George Michael 6
Freddie Perren 6
Norman Whitfield 6

https://en.wikipedia.org/wiki/List_of_Billboard_Hot_100_chart_achievements_and_milestones#Songwriters_with_the_most_number-one_singles