I agree what you are trying to say but Wiles's proof of Fermat's Last Theorem is not an idea but it finished product. It took Wiles years to finish the proof. If he told someone about the idea behind the proof in the initial phase without anything concrete and was not able to finish the proof, do you think the idea would be perceived?

> Wiles's proof of Fermat's Last Theorem is not an idea but it finished product

I don't think that distinction is the relevant one. The point is that it extended existing thought, rather than overturning it.

> If he told someone about the idea behind the proof in the initial phase without anything concrete and was not able to finish the proof, do you think the idea would be perceived?

I'm not sure what you're asking here. There's a reason mathematics journals are only interested in finished theorems rather than idle speculation, but I don't see how that's relevant.

If you don't think Wiles was rocking the boat, then I am not sure what qualifies in your opinion.

I already answered this. Wiles' proof didn't overturn anything, it only extended what was known. Again, as far as I know, it was celebrated by everyone in the field. No career was ended by the discovery.

Examples of a developments that rocked the boat would be the theory of evolution, quantum mechanics, and irrational numbers. [0]

[0] https://en.wikipedia.org/wiki/Irrational_number#Ancient_Gree...

He was clearly rocking the boat. His career was only not ended because he went so smartly about what he was doing.

I don't know what you're talking about. Wiles received an avalanche of awards for his achievement.

https://en.wikipedia.org/wiki/Andrew_Wiles#Awards_and_honour...

Yes, once he had proved it. You usually get an avalanche of awards once you successfully rocked the boat.

There was a long time where he didn't have a proof yet, but it was OK, because he told no-one that he was actually working on one. If he had told people openly that THIS what he chose to spend his time on, without actually having the proof yet, he would have been ridiculed, because it seemed like such an utterly hopeless enterprise at the time.

By rock the boat, I mean a discovery/publication that bothers a lot of people in the field. I am not referring to major breakthroughs in general.

Wiles' discovery was a tremendous breakthrough, but it didn't upset anyone. Another example of an entirely uncontroversial breakthrough is [0]. This is in contrast to the three examples of controversial discoveries that I gave above.

> If he had told people openly that THIS what he chose to spend his time on, without actually having the proof yet, he would have been ridiculed, because it seemed like such an utterly hopeless enterprise at the time.

I'd hope the field would be supportive of 'long shot' projects like this, but sure, I could believe many mathematicians would be skeptical.

[0] https://www.quantamagazine.org/computer-scientists-break-tra...