In his beautiful (but difficult) book "Complex cobordism and stable homotopy groups of spheres", concerned mostly with methods of computing homotopy groups of spheres, D. Ravenel describes a general method of producing elements on the $E_2$-page of Adams-Novikov spectral sequence. Later he discusses whether the so-called Greek letter elements descent to non-trivial elements in stable homotopy groups of spheres, ending with a rather curious remark which I quote in it's entirety.
In the intervening time there was a controversy over the nontriviality of $\gamma _{1}$ which was unresolved for over a year, ending in 1974 (see Thomas and Zahler [1]). This unusual state of affairs attracted the attention of the editors of Science [1] and the New York Times [1], who erroneously cited it as evidence of the decline of mathematics.
Can someone shed some more light on this matter? Why did the editors of New York Times become interested in the state of our knowledge of stable homotopy groups of spheres? Why would inability to determine whether a highly-complicated element (coming from an extremely complicated spectral sequence) is non-trivial be considered "decline of mathematics"?
Best Answer
The article in Science is entitled 'Mathematical Proofs: The Genesis of Reasonable Doubt'. It is essentially about proofs that are so long that "that they can never be written down, either by humans or by computers".
Regarding the $\gamma$ family, the relevant quote is just a short paragraph
This was followed by a letter by Zahler the next month.