We can never actually run such a test but we can try the thought experiment. Even if you are one of the "greats," most of your theorems, even the best and most surprising, would have been eventually proved a few months or a few years later. Other theorems would never have been proved because no one, other than the non-existent you, would have cared. Other than speeding up science a little bit, you cannot get a long-term individual impact on the field solely by proving theorems.
But proving those theorems builds your reputation and with that reputation you can shape the direction of the field. With this reputation you can, for better or for worse, help shape the direction of the field and set the research agenda for a generation of young graduate students. You also have lasting influence through your graduate students and the undergrads you convince to study computer science.
We can run this thought experiment the other way. Suppose many years ago a sperm darted right instead of left and fertilized an egg that hatched a true genius in our field. How much difference could that one person have made on our research and our lives?
Nobody is that important.ReplyDelete
I'm not sure how much information the comparison test would even give us (supposing that it could be done). For example, how would we relate to the world were Turing machines were never made, but in its place we have Curry machines?ReplyDelete
What if that lead to the introduction of iPods sooner but interactive proof systems later? We'd find it hard do anything other than enumerate the differences. Also, social issues would be a very wild variable.
A world without Einstein might have been a WWII without the atomic bomb, and that might have made everything else so radically different that nothing else would matter.
It's true that many inventions are, more or less, spawned by their zeitgeist. For instance, the WWW with or without Tim-Berners Lee would have been invented at some point, and actually his was one of several proposals in the same direction.ReplyDelete
However, some really important discoveries were made by geniuses that can see way above their times, such as Da Vinci, Galileo or Plato. The rest of us, can contribute little ideas that help to advance science.
We are six billion people at this time, and about 5-10 million active researchers. We're not enough to be a system in which individual ingenuity does not count.
A classic(al) example of someone way ahead of his time in this way is Archimedes. There is substantial evidence that he had derived many of the tools of calculus nearly 2000 years before Newton and Leibnitz.ReplyDelete
In the modern connected world where we tend to be aware of the goals and approaches of the other researchers around us it seems unlikely that there is as much dependence on individual insight. On the other hand there are many instances of relatively easy proofs (in retrospect) that have escaped researchers for 20 years and more. The individual still does seem to matter at least at the level of these relatively short time scales.
Gauss is another person reputed to have been ahead of his time. His notes are reputed to contain results and ideas that were not explored by other mathematicians until 50-100 years after his death.ReplyDelete
Even this definition of impact is doubtful. If there were two genius twins that advanced science in thousands of years, but each of them could also have done this on her own. Would that mean that both of them have zero impact?ReplyDelete
More generally, if you were part of a group of few people that together advanced the field, then even if each individual member of the group is replacable, I think you have the right to feel as if you had a lot of impact.
It's true that it seems that everything will be proven eventually, but as we all know, efficiency and time constraints make a lot of difference.
"Even if you are one of the "greats," most of your theorems, even the best and most surprising, would have been eventually proved a few months or a few years later."ReplyDelete
I think that this would not apply to some "greats". For instance, Wiles and Perelman spent about SEVEN years in isolation working on their proofs. I doubt that anyone would have solved either of these problems for decades had not these two adventurous souls decided to tackle these problems.