[jean23]

My favourite example is number theory, which was either hailed or ridiculed for millennia as being pure mathematics that can and will never be applied to real life problems.

Today number theory is the basis for several important fields of application, including computation theory, modern cryptography, and numerical calculation.

[roca]

Yes, but the question is, did developing number theory hundreds of years in advance of its applications accelerate the development of, say, cryptography? Or would cryptographers have just worked out the number theory when they needed it? If it did accelerate the development of cryptography, how much acceleration did we get for that investment?

Also in modern times, especially, there is a big problem of discoverability. If the mathematical result you need for some application is buried in a thirty-year-old journal using unfamiliar terminology, what are the chances you'll find it and understand it when you need it? I venture to suggest that much of the time it's easier to re-derive the result than to find it.

[OnlineGladiator]

That's a good point, but I think a strong counter-example would be anything we get from satellites. We went to space for political reasons, but let's just say it was for the sake of science because it sure didn't solve any immediate problems for mankind. But it did create the technology for satellites, which allow us to better predict the weather and gives us GPS tracking, and other things as well. But imagine you wanted to develop a global tracking system, would your first thought be to invent satellites if they did not already exist? So it definitely does matter sometimes, although which times is obviously open to interpretation.

[roca]

I think that is a weak counter-example. The applications of rocketry and satellites were obvious by the end of WW2. In 1945 Arthur C. Clarke had already published an article explaining how useful it would be to have communication satellites in geostationary orbit, and it didn't take much imagination to suppose that a big enough rocket could put them there.

[OnlineGladiator]

It's easy to think of it as a possibility, but the amount of effort to put a satellite into space is still extraordinary (space travel is still far from a commodity all these decades later). My point was they would not go through the trouble of first creating satellites as it would be considered too exotic of an idea. It would be like thinking of Uber 15 years ago before smartphones were ubiquitous, and deciding you first need to invent the smartphone rather than shelve the idea.

[naasking]

> Or would cryptographers have just worked out the number theory when they needed it?

Not a chance.