James Maynard appears regularly on Numberphile so if you'd like to hear some accessible mathematics from one of the authors of this paper I suggest you check it out:
Unfortunately, they award it on the 4n+2 years. As someone born on a 4n+0 year, I’ll have just 38 years, which is too severe a disadvantage for me to stomach, so I didn’t bother with it.
I went over this table of Fields Medal winners [1] and the 4n+2 people have won 28% of the awards. However, 33% of the awards were won by 4n+3 people but only 17% were won by 4n+0 people.
So your hypothesis does seem to bear out: people born on 4n+0 years are at a significant disadvantage for winning a Fields medal.
Pierre de Fermat wrote his "last theorem" (that no three positive integers a, b, c satisfy a^n + b^n = c^n for integer values of n>2) in the margin of a copy of Diophantus' arithmetica with the comment that "I have a truly marvelous proof which this margin is too thin to contain".
The theorem went unproved for 385 years until Andrew Wiles eventually proved it in 1995, winning the Abel prize (because he was too old to win a Fields medal). Most people think Fermat didn't have a proof - just an intuition - as Wiles' proof uses a bunch of extremely sophisticated and powerful results that came well after Fermat.
The GP's comment is particularly clever because until Wiles, the Riemann hypothesis and Fermat's last theorem were the two most famous unsolved problems in maths, so were often talked about together as being these almost unassailable challenges.
Yes, I don't think the Fields medal was intended as the "Nobel prize of mathematics", but since it was the biggest award that existed it got promoted as such despite its inequivalence. More recently there's the Abel prize, which tries to be a more direct Nobel prize analogue, but of course the Fields medal has a multi-decade head start in terms of promotion...
Nobel Prize (and Abel Prize and Wolf Prize) are for the lifetime achievement, i.e. the scientific contributions that lead to the prize might be from decades ago.
https://www.youtube.com/playlist?list=PLt5AfwLFPxWJdwkdjaK1o...