First, for as much as I love MBTI, I believe it has its flaws, or moreover our ability to comprehend it organically in action (and apart from our own type specific myopia) is very limited. Coming to MBTI as a derivative of Jung's works is even further removed from a pure understanding (albeit if there's one). But I'm grateful that we have this to provide such interesting dialog as can be afforded thanks to these predecessors.
A few points just felt too mechanical for me as far as a working comprehension goes. To my shame *this INTP just couldn't leave alone.
So, yeah, as one who grew up with and knows many INTJs, I had to laugh at; "His discoveries rely more on insight than logic". Not because this isn't true (not going there, will just accept and move on), but because I don't think I would use this to support a case for an INTJ Isaac. Although I certainly see that you could. But there were a few things that I wanted to clear up.
In my opinion, INTPs are more insightful than INTJs, if by insight we mean gaining a "clear" perception into a thing, and to that end I don't know how to separate logic from this. But this is not to downplay their great strengths which can cast many an INTP in the shadows (I'm speaking generically here of course). But this is because T(i), which we (INTPs and ENTPs) both share, is more 'logical' as you say (although that's not quite what I infer by it). But this lends to clearer insights in a lot of ways than T(e) is willing to allow. This is not necessarily confining T(e) to what it is capable of (although sometimes this can be the case), but what I've noticed is a bent that is usually too busy pushing forward and out (especially when paired with the J). Not to mention N(i) pulls its insights in a subjective manner towards the object it is dealing with. This can isolate it, as compared to N(e) which randomly explodes it.
These insights drive the J power house forward, but it isn't always leading to a better or more congruous understanding if you will. The J wants to move forward, the T(e) wants something workable and usable outside of himself, and the N(i) master tends to isolate multiple streams of insight onto a single target. It's not as inertial and much more attenuated insight from my experience and reading than an N(e) feeding a T(i) chore will provide.
I think we get this 'logic' label on the INTP with his T(i) dominated core, and I can understand applying 'insight' to a N(i) dominate. However, I just felt like this deserved to be fleshed out with a little more body to it. Because we cannot surmise a whole and working functionality of a type or individual by merely comparing two traits, albeit even their dominate ones. Although comparing single traits is still very helpful.
While N(i) may do very well dealing with a closed system they don't always have the 'insights' as to how that system connects in a non contradictory fashion to criteria outside that system. And with T(e) as auxiliary this is even more the case. And let's face it, little is isolated to this degree, certainly not on the quantum level and this is why INTPs do make such great physicist and scientist. A great exception to this where N(i) is concerned can be found in the INFJ, where they still have that dominate N(i) but a tertiary T(i) to direct this.
It's just not in the same way T(i) caters to the insights it develops though (adding to their 'logical' whole). I have 2 INTJ brothers and several INTJ friends. They are all about getting things hammered out; nailing down the procrustean bed so to speak. ENTJ's are even worse (I say this coming from the disposition of sequestering gainful insights) not to the apprising of such traits on the whole. In the grand scheme such traits pull a double as their blessing and cursing all rolled into one.
Much to the same degree that T(i) is my greatest bane as it is where I may show the most aptitude. Since T(e) is external it is actually considered more objective if you will than T(i), however, again, here it's easy to misrepresent this. Where they are objective and where they are subjective are pretty much in just the opposite arenas (shadow functions to boot).
I will definitely give you mathematics though as a bent to the T(e), however in applying this as Isaac does this is more indicative of an INTP to see how this 'system' applies, wait for it....'theoretically' to the outside world; 'physics' if you will. Certainly though points could be made for both cases. I just felt like this reasoning was actually a bit askew. Working directly with numbers like that is actually pretty T(e)J, even when it remains only mathematical if you will. Applying this to the literal world makes more sense to an INTP because his theory does not exist isolated as it could to the N(i)T(e)J, where the concrete numbers themselves represent what is tangible and external. There right there in front of him or on paper and he can deal with them. As to the INTP such numbers are just an abstraction of reality, it represents something real, but it is itself not the real thing (nor does he have to play with this tangibly). He would be driven however to flesh this verisimilitude out into reality, not to deal with it, but to see if such a 'theory' holds up. So applying it to physics isn't really indicative of an INTJ, not necessarily, and I get a rather sneaking suspicion this is an INTP driven move. But I'm trying to not polarize on any two facets here either and for me the case is still out.
As an INTP I literally feel a part of everything around me in such a complete way it's scary. Except for people, at which point I really feel like the alien. I've want to lie stripped in freezing cold rivers at times (and have though I was clothed), or just in some way become one with what is around me (and in very odd ways at times). Not sexually speaking, I think I should clarify with that whole "become one" bit. Lol, but I can be standing on top of a high cliff and want to leap, or staring into the depths of the ocean and want to drown in the waves. Not that I want to die...It's quite odd and been this way from youth, but I understand it now as far as MBTI functionality can explain. My oddness is also something that's really driven me to understand these things a little more. It's a great sense of relief to me to know I'm not broken in ways that I thought I was. Though I can tell the jury is still out with many of my friends and family. I may have to clean my canvas, but I don't need a new one altogether.
Lol, I should probably extrapolate a little on this, but this is where I think a lot of people can misunderstand us INTPs. We live in our heads, true. We live in the realm of theory/abstraction, yes. We're highly intuitive and often unaware of our surroundings, or it would seem, but whatever were dreaming up in our heads, its connected, it has to be to the real world. That's because we really do see ourselves as the independent arbiters of reality. It's not theory to us, and that may sound arrogant, but we truly at times are trying to transcend any subjectivity so much so to the degree that we can feel like just raw bits of energy and matter projected out onto a stage, its all the same. And it all has to agree for us. We may not want to interact or push forward, but we do very much want to apply what is inside of us, not generally for the sake of anything, that would be subjective, but just to make sure we're harmonized with this 'whole' if you will. We want to make sure we're on the same channel as the rest of the universe, not as the rest of the people, uhck, how would they know?...This is unfortunately why many an INTP can become pretty grumpy. It's safe to say that we do look down on the subjectivity and 'smallness' of other types. Another area where MBTI has really helped me see the worth and value in EVERYONE'S uniqueness. I've always believed it, but I guess I was a doubting Thomas. Now I can see it with my own two eyes.
Hmmm, well, I think I took that off in a direction I had not intended. I will leave it though, I suppose it could be informational to some as to how at least this INTP would relate it. But what I'm trying to say is that we feel very connected with what's in our heads to the outer world. We're not trying to have reality surrender to our logic, but rather trying to surrender our reality to logic, and that's where the insight comes from. We see the two as congruous. I feel like INTJs and INTPs are ALWAYS acting on different suppositions, in debate I can rarely agree with an INTJs axiom and when I can again rarely with how they would apply it.
INTJs seem more connected to the external and are engaging it more adamantly, but the INTP reaches in and tries to conform what is inside to that which he believes is unifying truth to all that he sees, feels, touches, and hears externally N(e). The INTJ tries to form the external to match what logic he believes, and hence could in some ways be considered more logical on his subject matter and its relevancy. But the INTP is more objective in his approach to whatever he deems worthy of investigation. I guess it all depends on how you look at it and what presuppositions you're starting at. We could go all the way back to square one I suppose, and actually that's how myself as an INTP approaches most things, by going as far back as is necessary...This is why T(i) is MUCH slower than T(e), but will usually be more refined....they may just never settle on an answer though.
At least this is my experience as an INTP, so for me, I could have no interest looking at math from a strictly logical basis. And this is also why I've said they consider T(i) to be more subjective. Where is T(e) could literally take some dead numbers and work with them w/out direct attachment and meaning to themselves.
And this is where I think you could also make the argument for the INTJ concerning your point on mathematics applying it to say physics too because they could very well do the same thing as an INTP and for the very same reasons, or very different reasons. I'm not just throwing that out there either to cover my basis, it's very plausible I believe. It's really hard to know and there's always variation that type classification cannot account for. At least not in our limited understanding of how the brain and spirit works, people just don't fit into neat little boxes.
Of course even if we did, OTHER people couldn't ever fully understand the complexity and organizing systems of these boxes and how they all fit together (not even for ourselves). With that said, the few boxes that we can handle, I like to have fully fleshed out to the degree in which we can handle them.
I guess that's why I'm just not sure what you meant by insights vs logic if you're attributing insights to the INTJ and logic to the INTP. As far as dealing with the logic right in front of them I would say that an INTJ is going to be more adept. However, but give the INTP time to think on this and he will not miss ANYTHING that the INTJ might. He will take the time to draw more from his insights imo than the INTJ would. Even if the INTJ is fueled on insights or intuition if you will. Inspiration is funny like that too though. While intuition is much more abstracted and arbitrary, Thinking is not. The differences obviously being their introversion or extroversion, but also that the INTP is a Thinking core while the INTJ an iNtuiting one. It's hard to compare the two side by side or in isolation of complete functional analysis. I'm in no way implying this has been stated either. I say it to guard against my own words being understood as it's hard to speak of this on a whole w/out breaking it down bit by bit. My mind, however, understands it as a whole, so breaking it down is doubly hard for me. Seeing the big picture is much easier. I thank whoever muddled through this, and hope that if they are interested in this as am I, it was not a total waste of their time. Even if they disagree as well as I'm aware that my communication was rather poor and choppy at times, thank you.