I agree that people do often make major discoveries alone. I also agree that “committees” truly could not have made many of those discoveries. But I the other thing I think is true is that they still only do it when the supporting ideas become available to them. Not just the observations, but the right ways of thinking and asking questions about those observations. Newton talked about “the shoulders of giants” and all that.
Once the conditions exist, you’ll get your genius reasonably soon. There are enough geniuses out there to make things happen when the time is right.
If Einstein hadn’t come up with, say, relativity, somebody else probably would have within 10 or 20 years. Maybe even a few people, who indeed might have been doing things more like “working alone and occasionally communicating”, than “collaborating closely”. On the other hand, I very much doubt that Einstein himself would have arrived at even Special Relativity if he’d been working 50 or 100 years earlier.
Thiel seems to be arguing against that by suggesting that the proof Fermat’s Last Theorem just lay there as a “secret” for 358 years, until Wiles Heroically Challenged The Orthodoxy that refused to accept that it Could Not Be Done. I think that misstates the matter very badly, and that all the Thiel text is really unconvincing.
At least as Iunderstand the history, Wiles was indeed living in a mathematical community that was pretty discouraged about proving Fermat’s Last Theorem… but nonetheless he was using a huge apparatus of number theory that had been built up over those 358-or-whatever years. Wiles didn’t prove the theorem using tools that would have been available 350 years before (and nobody believes that Fermat himself ever had a correct proof). The bit Wiles filled in was the proof of the Taniyama-Shimura-Weil conjecture. To even state that conjecture, let alone prove it, you have to use a bunch of concepts to which Fermat’s era had no access.
So Wiles’ proof wasn’t simply unnoticed for 350 years until he mystically “discovered a secret”. Thiel’s presentation reads as sloppy, clueless, or even dishonest, on that matter. It also seems kind of clueless on the true value of what Wiles did. Although I’m sure Wiles was very much motivated by wanting to nail Fermat’s Last Theorem, the framework he developed to do that also advanced mathematics in general, and that’s more important in the grand scheme of things.
As for Wiles keeping a secret, a 6-year secret is a very different matter from a 358-year secret. The field may have been demoralized enough, or maybe the solution was just truly inobvious enough, to give Wiles 6 years or more… but it wouldn’t have taken another 350 years if Wiles hadn’t done it. I suspect it wouldn’t have taken 50 or even 20.
Also, when Wiles went public in 1993, what he had was wrong (and the theorem had a long history of false proofs at that point). It took Wiles another year to fix the problems other people found in his proof.
As for Mullis, PCR is a laboratory technique, not a sweeping framework. I don’t think it puts Mullis in Wiles’ league, let alone Einstein’s or Newtons. And Mullis really does seem to have just mostly lucked into noticing it. I’m thinking it would more likely have been under 5 years than over 10 before somebody else came up with PCR. And I’m not entirely sure that a committee couldn’t have come up with PCR given a driving application, so I think Mullis is actually a poor example.
What you say is even more true than you think. We would have had “relativity” in 1906, if you are satisfied with an experimentally indistinguishable theory which kept the ether as a conventional choice (a degree of difference similar to the one between interpretations of quantum mechanics). Poincaré had already submitted a paper in 1905 before seeing Einstein’s, building on Lorentz’s previous work. Now, Einstein’s theory is preferable for several reasons, but ultimately the difference is small.
If you look you find similar stories for Newton, Mendeleev, obviously Darwin, and others. There are some counterexamples, but ultimately we should take Newton seriously: the height of the shoulders you stand on is more important than your own for determining how far you can see.
I had a look at my copy of Simon Singh’s “Fermat’s last theorem” (amazing book by the way) and three things are pretty clear :
Wiles’ proof makes extensive use of papers published in the years 1986-1993 while he was working on his proof, so he was certainly not isolated during this time.
he was unable to find the error in his proof, and had help from Taylor to correct the error.
So if he had not been so obsessed with “being the one to prove Fermat’s last theorem”, the proof would have been finished a couple years sooner.
So yeah, the lonely genius is a myth and a dangerous one. Long live the collaborative genius who works with his fellow geniuses !
Well said and I largely agree with your assessment of Mullis. One thing to consider: there is some added value in getting discoveries sooner (e.g. something with medical implications, like PCR). I also wonder about the contingency/path-dependence of science/tech on large scales—if it had been discovered at another time by another person would science (and history) have followed the same path?
On a broader level, I wonder how science/tech contingency interacts with the contingency of culture and history as these set what people value and care about in the first place, in turn affecting what people study/build. I think about how the history of science and biology would be different over the last 150 years if we only had Wallace and not Darwin. Wallace was not nearly as respected as Darwin, didn’t have nearly as much evidence behind as theory, and had a more theological framing on Natural Selection. I wonder how what what the ripple effects would be today if we only had Wallace and not Darwin
On this I agree with you. But the Darwin issue is a bit of a special case—the topic was politically/religiously charged, so it was important that a very respected figure was spearheading the idea. Wallace himself understood it, I think—he sent his research to Darwin instead of publishing it directly. But this is mostly independent of Darwin’s scientific genius (only mostly, because he gained that status with his previous work on less controversial topics).
On the whole, I agree with jbash and Gerald below—“geniuses” in the sense of very smart scientists surely exist, and all else equal they speed up scientific advancement. But they are not that above ordinary smart-ish people. Lack of geniuses is rarely the main bottleneck, so an hypothetical science with less geniuses but more productive average-smarts researchers would probably advance faster if less glamorously.
You could make a parallel between geniuses in science and heroes in war: heroic soldiers are good to have, but in the end wars are won by the side with more resources and better strategies. This does not stop warring nations to make a big deal of heroic exploits, but it’s done to improve morale mostly.
I agree that people do often make major discoveries alone. I also agree that “committees” truly could not have made many of those discoveries. But I the other thing I think is true is that they still only do it when the supporting ideas become available to them. Not just the observations, but the right ways of thinking and asking questions about those observations. Newton talked about “the shoulders of giants” and all that.
Once the conditions exist, you’ll get your genius reasonably soon. There are enough geniuses out there to make things happen when the time is right.
If Einstein hadn’t come up with, say, relativity, somebody else probably would have within 10 or 20 years. Maybe even a few people, who indeed might have been doing things more like “working alone and occasionally communicating”, than “collaborating closely”. On the other hand, I very much doubt that Einstein himself would have arrived at even Special Relativity if he’d been working 50 or 100 years earlier.
Thiel seems to be arguing against that by suggesting that the proof Fermat’s Last Theorem just lay there as a “secret” for 358 years, until Wiles Heroically Challenged The Orthodoxy that refused to accept that it Could Not Be Done. I think that misstates the matter very badly, and that all the Thiel text is really unconvincing.
At least as Iunderstand the history, Wiles was indeed living in a mathematical community that was pretty discouraged about proving Fermat’s Last Theorem… but nonetheless he was using a huge apparatus of number theory that had been built up over those 358-or-whatever years. Wiles didn’t prove the theorem using tools that would have been available 350 years before (and nobody believes that Fermat himself ever had a correct proof). The bit Wiles filled in was the proof of the Taniyama-Shimura-Weil conjecture. To even state that conjecture, let alone prove it, you have to use a bunch of concepts to which Fermat’s era had no access.
So Wiles’ proof wasn’t simply unnoticed for 350 years until he mystically “discovered a secret”. Thiel’s presentation reads as sloppy, clueless, or even dishonest, on that matter. It also seems kind of clueless on the true value of what Wiles did. Although I’m sure Wiles was very much motivated by wanting to nail Fermat’s Last Theorem, the framework he developed to do that also advanced mathematics in general, and that’s more important in the grand scheme of things.
As for Wiles keeping a secret, a 6-year secret is a very different matter from a 358-year secret. The field may have been demoralized enough, or maybe the solution was just truly inobvious enough, to give Wiles 6 years or more… but it wouldn’t have taken another 350 years if Wiles hadn’t done it. I suspect it wouldn’t have taken 50 or even 20.
Also, when Wiles went public in 1993, what he had was wrong (and the theorem had a long history of false proofs at that point). It took Wiles another year to fix the problems other people found in his proof.
As for Mullis, PCR is a laboratory technique, not a sweeping framework. I don’t think it puts Mullis in Wiles’ league, let alone Einstein’s or Newtons. And Mullis really does seem to have just mostly lucked into noticing it. I’m thinking it would more likely have been under 5 years than over 10 before somebody else came up with PCR. And I’m not entirely sure that a committee couldn’t have come up with PCR given a driving application, so I think Mullis is actually a poor example.
What you say is even more true than you think. We would have had “relativity” in 1906, if you are satisfied with an experimentally indistinguishable theory which kept the ether as a conventional choice (a degree of difference similar to the one between interpretations of quantum mechanics). Poincaré had already submitted a paper in 1905 before seeing Einstein’s, building on Lorentz’s previous work. Now, Einstein’s theory is preferable for several reasons, but ultimately the difference is small.
If you look you find similar stories for Newton, Mendeleev, obviously Darwin, and others. There are some counterexamples, but ultimately we should take Newton seriously: the height of the shoulders you stand on is more important than your own for determining how far you can see.
I had a look at my copy of Simon Singh’s “Fermat’s last theorem” (amazing book by the way) and three things are pretty clear :
Wiles’ proof makes extensive use of papers published in the years 1986-1993 while he was working on his proof, so he was certainly not isolated during this time.
he was unable to find the error in his proof, and had help from Taylor to correct the error.
So if he had not been so obsessed with “being the one to prove Fermat’s last theorem”, the proof would have been finished a couple years sooner.
So yeah, the lonely genius is a myth and a dangerous one. Long live the collaborative genius who works with his fellow geniuses !
I don’t even understand what Thiel is trying to say, which is pretty typical.
Well said and I largely agree with your assessment of Mullis. One thing to consider: there is some added value in getting discoveries sooner (e.g. something with medical implications, like PCR). I also wonder about the contingency/path-dependence of science/tech on large scales—if it had been discovered at another time by another person would science (and history) have followed the same path?
On a broader level, I wonder how science/tech contingency interacts with the contingency of culture and history as these set what people value and care about in the first place, in turn affecting what people study/build. I think about how the history of science and biology would be different over the last 150 years if we only had Wallace and not Darwin. Wallace was not nearly as respected as Darwin, didn’t have nearly as much evidence behind as theory, and had a more theological framing on Natural Selection. I wonder how what what the ripple effects would be today if we only had Wallace and not Darwin
On this I agree with you. But the Darwin issue is a bit of a special case—the topic was politically/religiously charged, so it was important that a very respected figure was spearheading the idea. Wallace himself understood it, I think—he sent his research to Darwin instead of publishing it directly. But this is mostly independent of Darwin’s scientific genius (only mostly, because he gained that status with his previous work on less controversial topics).
On the whole, I agree with jbash and Gerald below—“geniuses” in the sense of very smart scientists surely exist, and all else equal they speed up scientific advancement. But they are not that above ordinary smart-ish people. Lack of geniuses is rarely the main bottleneck, so an hypothetical science with less geniuses but more productive average-smarts researchers would probably advance faster if less glamorously.
You could make a parallel between geniuses in science and heroes in war: heroic soldiers are good to have, but in the end wars are won by the side with more resources and better strategies. This does not stop warring nations to make a big deal of heroic exploits, but it’s done to improve morale mostly.