No history actually tells you that only 1% of produced maths is useful. You only see the good stuff not the ugly stuff.

I don't know why people are throwing around percentages so much in these replies. Percentage of what? Plus, the body of work of mathematics continues to grow all the time.

The core of the original comment that started this chain was:

> Applications of pure math happen downstream decades or centuries later.

My argument was that history shows that a surprising amount of mathematics does eventually trickle down into applications. I don't think anyone is arguing all of mathematics eventually sees an application.

Again, my point was that history does indeed seem to show that "applications of pure math happen downstream decades or centuries later". As the original commenter said, it's hard to predict what will be the next thing to be applied.

In addition to what the other commenter said, it’s important to understand the scale. Cutting edge research 600 years ago was solving cubic equations. Today, cutting edge research requires potentially years of advanced study to understand the objects involved.

There are more mathematicians alive today than at any point in human history, and their work has become specialized to a tremendous degree. Gone are the days where one mathematician could do substantial new work in a dozen diverse areas.

So, in short, the fact that historically lots of pure math has not found use, the specialized nature of modern research math, the volume of work being out out, and an irreverence for applications(again, this is _pure_ math) leads me to be doubtful that even a moderate amount of modern pure math research will ever be useful in any practical sense.

I've read lots of math papers that were a complete waste of time because they were banal. The only "innovation" was to use different words to describe the same thing. New mathematics is actually pretty damn hard I suspect.