I’ve had the opposite experience (though restricted to problems that someone at all has solved/understood). There are multiple fields (such as AI/ML, cryptocurrency, and zero-knowledge proofs) that I at some point thought were mysteriously difficult. In each case, there is a finite set of important concepts (less than 30) to learn, and it is possible to do cutting-edge research from there.
As far as I can tell, nothing is magic. Nothing that anyone can do is mysteriously difficult. Complicated things that anyone understands decompose into a finite number of interacting parts, each of which (as well as their interactions) can be modeled. Skills people have (even ones they don’t understand) can be learned through experience and guides; getting great can take years, but getting adequate usually only takes months. Actually doing any of these requires willingness to understand and think for yourself. If you don’t know if you can understand a field, you can set aside an amount of time, such as one month, to intensively study it, and see what happens.
(Of course, some things can be so hard that no one knows how to do them, and these actually can be mysteriously difficult, though won’t be with the benefit of hindsight if someone actually does them. And all of this is based on my own personal experience.)
Glad that this approach worked out for you! It’s an amazing feeling when you finally solve or get something that looked so hard initially. I would not deny that this has happened to me, too, but mostly in the cases I knew for sure I could handle with enough effort. I did my PhD in General Relativity, and had to go through a few proofs that required significantly more background than I had at the time. I was able to master the necessary basics of Algebraic Topology enough to add my own small theorem on top of what was already in my research area, yet it was excruciatingly slow and painful to get to that point, and not a lot of fun. I had to abandon any larger ambitions in the area. Similarly, I was used to getting A and A+ in almost all my undergrad and grad classes, yet when I hit advanced grad classes, like String theory and topics in QFT, I was lucky I could get through them, even though other grad students seemed to have had little difficulties there.
In general, I have found that in many areas, especially in math, everyone has their threshold of abilities. Below the threshold the effort required scales basically linearly with the amount of material, Past that threshold any extra learning becomes exponentially more difficult. I mean “exponentially” in the mathematical sense, not in the colloquial one. Gotta know your limits.
I’ve had the opposite experience (though restricted to problems that someone at all has solved/understood). There are multiple fields (such as AI/ML, cryptocurrency, and zero-knowledge proofs) that I at some point thought were mysteriously difficult. In each case, there is a finite set of important concepts (less than 30) to learn, and it is possible to do cutting-edge research from there.
As far as I can tell, nothing is magic. Nothing that anyone can do is mysteriously difficult. Complicated things that anyone understands decompose into a finite number of interacting parts, each of which (as well as their interactions) can be modeled. Skills people have (even ones they don’t understand) can be learned through experience and guides; getting great can take years, but getting adequate usually only takes months. Actually doing any of these requires willingness to understand and think for yourself. If you don’t know if you can understand a field, you can set aside an amount of time, such as one month, to intensively study it, and see what happens.
(Of course, some things can be so hard that no one knows how to do them, and these actually can be mysteriously difficult, though won’t be with the benefit of hindsight if someone actually does them. And all of this is based on my own personal experience.)
Glad that this approach worked out for you! It’s an amazing feeling when you finally solve or get something that looked so hard initially. I would not deny that this has happened to me, too, but mostly in the cases I knew for sure I could handle with enough effort. I did my PhD in General Relativity, and had to go through a few proofs that required significantly more background than I had at the time. I was able to master the necessary basics of Algebraic Topology enough to add my own small theorem on top of what was already in my research area, yet it was excruciatingly slow and painful to get to that point, and not a lot of fun. I had to abandon any larger ambitions in the area. Similarly, I was used to getting A and A+ in almost all my undergrad and grad classes, yet when I hit advanced grad classes, like String theory and topics in QFT, I was lucky I could get through them, even though other grad students seemed to have had little difficulties there.
In general, I have found that in many areas, especially in math, everyone has their threshold of abilities. Below the threshold the effort required scales basically linearly with the amount of material, Past that threshold any extra learning becomes exponentially more difficult. I mean “exponentially” in the mathematical sense, not in the colloquial one. Gotta know your limits.