As the article said, none really. It's more the tools that were created to solve it that are useful. FLT is like the Apollo mission of Mathematics and has been for hundreds of years. A crazy dream of no direct immediate practical value, but the pursuit of which sparks innovation and dreams.

What's interesting about FLT is that in the sense of proving a hypothesis, although the attempts themselves have lead to failures in their objective, they often illuminated whole new areas of mathematics, but this realization only comes somewhat later than when the proof is realized. It was obvious that a particular attempt had failed relatively quickly, but the lessons learned and their applications required a keen (creative mathematical) eye to spot.

Badiou (a continental political philosopher interested in the philosophy of mathematics) uses FLT as an example in political contexts, to what extent we can say that a utopian vision has failed even if it results in disaster, we should be (and some have been) looking out for the lessons which are learned after failure.

That last sentence about Badiou, whoever that is, was a sharp turn to the left.

Human as an individual is not a number. Yes may be for the philosopher king for an ideal which not everyone agree or vote for may or may not come or forever waiting, we just kill millions and millions.

Maos has it and starve 30 millions.

Soviet Union.

USA has its Vietnam and 2nd Iraq war.

I am not saying we should not try but Great Saint begot Great Thief. Be afraid of people who sit in their arm chair and talk about scarifie for the ideal.