The first record I found of this photograph is in <A HREF="https://books.google.nl/books?id=7QexAAAAQBAJ">Oxford Figures: Eight Centuries of the Mathematical Sciences</A>. Professor Michael Atiyah shares some recollections of J.H.C. Whitehead and his pigs:

<IMG SRC="https://ilorentz.org/beenakker/MO/Whitehead.png" WIDTH="500"/>

<sub>See also an interview with Atiyah at <A HREF="https://www.maths.ox.ac.uk/node/903">Oxford Mathematics Interviews.</A> (Whitehead and pigs enter at the two-minute mark.)</sub>

This might explain why Whitehead liked pigs:

• *Henry Whitehead, whose school of topology attracted scholars from around the world, was a keen pig farmer: **he claimed to derive mathematical inspiration by scratching his pigs’ backs for an hour every afternoon.***    
<sub>source: <A HREF="https://www.maths.ox.ac.uk/system/files/legacy/3277/newsletter_0414_0.pdf">Oxford Mathematical Institute Spring Newsletter</A></sub>