I second this and would add that it's really easy to catastrophically forget things in math. I'm pretty sure that most CS knowledge I have I will retain at a level where I won't forget the general ideas and re-reading materials can quickly refresh the details. This is not true for advanced math. I did a pure math PhD and my own thesis is impenetrable to me 20 years later. It would take months, if not years, of focused effort for me to regain the understanding.

"tcp" can take roughly 3-4 weeks of heads-down dedicated study to have some reasonable familiarity with. Same is true with most of the other concepts. Being able to speak with expertise on that list of topics is 3-4 years of really focused study and work.

I think what happens is that people often have passing familiarity with a word or topic and presume knowledge, and years (decades) later they realize they knew almost nothing.

I will say that Mathematics is different (for me at least) because unlike the infrastructure computing concepts (IETF type, not IEEE)- which mostly require studying, lab work, and some coding to get your hands dirty - advanced math is just ... really hard. There are IQ issues at play.

Obviously a lot of computing turns out to be mathematics - so there is clearly convergence/overlap as well...

I think one of the key differences is that math is abstract whereas CS is relatively concrete.

CS examples are often easy to picture and understand the motivation for. You can use tools to visualize or play around with them and test them.

Math gets abstract so fast you have to spend a week of research to even understand the problem statement. The the motivations themselves can be completely unclear until you have a lot of context.

I majored in math (B.S.) and upper level math is completely foreign to me.

As a counterpoint, i've worked with enough math PhD's over my career who couldn't wrap their head intuitively around many concepts from software engineering, while others had no problems in doing so even from folks without any stem background. We often undererstimate how much field knowledge we aquire over the years and overestimate how easy it is for others to catch up.

Again, you are underestimating how much effort it takes to understand how an 8086 CPU works. There are a lot of foundational concepts that you are simply assuming the person already understands. That may be a reasonable assumption for a CS undergraduate, but the average person does not understand binary arithmetic, registers, memory addressing, instruction execution, calling conventions, or even what a CPU is doing at a meaningful level to even start to understand 8086.

Also, understanding an 8086 CPU is not even remotely comparable to the level of mathematics Terence Tao was discussing above. The 8086 is a relatively basic and concrete topic. You can build a workable mental model of it from a finite instruction set, a handful of registers, and a reasonably straightforward memory model.

From my perspective folks here on HN and in CS often think they should somehow be able to understand advanced mathematics papers at a glance, merely because they are good at basics of programming or computer science (8086). That is not how it works. Most mathematics is not inherently much harder than computer science; both fields require you to accumulate a large amount of foundational knowledge before advanced material becomes comprehensible.

There is an enormous amount of computer science that most programmers are completely unfamiliar with, especially within academic CS: programming-language theory, type theory, formal semantics, compiler theory, algorithmic research, complexity theory, distributed computing theory, verification, cryptography, computational geometry, numerical methods, and so on. Being proficient in one narrow area does not automatically give you the prerequisites for another.

A web developer would not be expected to casually understand a research paper on type theory or approximation algorithms without first learning the relevant notation, terminology, and foundational results. Mathematics is no different. The feeling that mathematical writing is uniquely impenetrable mostly comes from encountering it without the years of accumulated context that mathematicians have silently built-up.

I can show you a paper about an advanced algorithms or chip design, that is large made up of fundamental cs concepts and general physics and even you likely someone with pretty in-depth understanding of CS would find hard. There are orthogonal subjects, for instance my mathematician friends things I am insane reading so much about weird computing topics, and I find his research in some weird number theory thing completely mind-bending.

Try and explain to a lay friend how registers & isa works in-depth with all the details not a hypothetical higher level model so that they can understand the nuance of looking at assembly, limit it to 8086 perhaps, it will take significantly longer than a weekend.

Ofc Terence Tao and his level of intelligence is beyond me, I wouldn't compare but general advanced mathematics is not something folks here couldn't pick up if they actually tried to work on it, just give it a shot (though I would recommend don't start with advanced topics build up slowly I think most people can understand most maths papers even the bleeding edge ones within a few months of serious self-study, and won't even feel that it's after a few years, compare that to the time spent learning software and computing 6-8 hours a days for several years)...