Suppose you were a contemporary professor sent back in time. You need to continue your academic career, but you can’t let anyone know that you’re from the future. You can’t take anything material with you but you retain your memories.

At first thought you might think you could become a superstar, like the musician in the movie Yesterday who takes credit for songs by The Beatles. But on second thought, maybe not.

Maybe you’re a physicist and you go back in time before relativity. If you go back far enough, people will not be familiar with the problems that relativity solves, and your paper on relativity might not be accepted for publication. And you can’t just post it on arXiv.

If you know about technology that will be developed, but you don’t know how to get there using what’s available in the past, it might not do you much good. Someone with a better knowledge of the time’s technology might have the advantage.

If you’re a mathematician and you go back in time 50 years, could you scoop Andrew Wiles on the proof of Fermat’s Last Theorem? Almost certainly not. You have the slight advantage of knowing the theorem is true, whereas your colleagues only strongly suspect that it’s true. But what about the proof?

If I were in that position, I might think “There’s something about a Seaborn group? No, that’s the Python library. Selmer group? That sounds right, but maybe I’m confusing it with the musical instrument maker. What is this Selmer group anyway, and how does it let you prove FLT?”

Could Andrew Wiles himself reproduce the proof of FTL without access to anything written after 1971? Maybe, but I’m not sure.

In your area of specialization, you might be able to remember enough details of proven results to have a big advantage over your new peers. But your specialization might be in an area that hasn’t been invented yet, and you might know next to nothing about areas of research that are currently in vogue. Maybe you’re a whiz at homological algebra, but that might not be very useful in a time when everyone is publishing papers on differential equations and special functions.

There are a few areas where a time traveler could make a big splash, areas that could easily have been developed much sooner but weren’t. For example, the idea of taking the output of a function and sticking it back in, over and over, is *really* simple. But nobody looked into it deeply until around 50 years ago.

Then came the Mandelbrot set, Feigenbaum’s constants, period three implies chaos, and all that. A lack of computer hardware would be frustrating, but not insurmountable. Because computers have shown you what phenomena to look for, you could go back and reproduce them by hand.

In most areas, I suspect knowledge of the future wouldn’t be an enormous advantage. It would obviously be *some* advantage. Knowing which way a conjecture was settled tells you whether to try to prove or disprove it. In the language of microprocessors, it gives you good branch prediction. And it would help to have patterns in your head that have turned out to be useful, even if you couldn’t directly appeal to these patterns without blowing your cover. But I suspect it might make you something like 50% more productive, not enough to turn an average researcher into a superstar.

You just need to do research in topics that are relatively modern but still quite elementary: Operations Research, Game Theory, Graph Theory, Information Theory, etc. are good candidates.

Why would you be an academic when you could remember, from your general life circumstances, which technologies and business ideas would work? You’d make unlimited money, and then you could fund whole institutes to work in the directions you know are promising, even if you don’t get the specifics.

@Carlos: I agree that the topics you mention are similar to chaos etc. Low barrier to entry. I suppose the logical prerequisites were there, but not the motivation. For example, electronic communication motivated information theory and WWII motivated operations research.

@Tomas: I addressed technology in the post, but I hadn’t thought about business ideas. Maybe ideas like modern management techniques could give you a big advantage.

Similar to math ideas, I suspect that business ideas would be a multiplier, not a gold mine. Maybe they could make you 50% more effective. But if that compounds, it could be huge.

I also wonder how many business ideas that seem inevitable to us would not translate well to an earlier time.

I would just tell them my definition of funcoids and the generalized limit of an arbitrary function at every point. It is so easy that a child could be able to remember it.

Modern people ignore me as if I were from the future… Everybody ignores this “revelation”.

https://math.portonvictor.org/

I vaguely remember a classic SF story by William Tenn entitled “Flirgleflip” that plays on this theme. The man claiming (truthfully) to be from the future can’t even explain to the people in the past what he did in the future; there aren’t enough referents.

You could break the permutation cipher in Roman times, which only requires letter frequency analysis. It might have been good enough to motivate early consideration of statistics as well.

But that’s the only one I can think of; kinda proving your point.

Hilarious standup on the same topic: https://youtu.be/QXy3uII-xn0