https://www.maths.tcd.ie/pub/Maths/Courseware/ProblemSolving...
> Mathematics is a part of physics
> What about the next 3,900 words after the first sentence?
I also have a degree, but mostly taught myself the important undergrad-level concepts as a kid. I just went to the library and borrowed any of the hundreds of books written to clearly communicate maths to beginners or downloaded any of the free ebooks / lecture notes.
Name a single field of endeavor that is more open in 2026. Software certainly isn't one of them - the best stuff has always been gatekept.
But also, with things rapidly changing, perhaps in ten years chat programs will not only do superhuman but make their proofs marvelously accessible and provide incredible tutoring sufficient to bring any curious up to a super high level quickly. Then what can you say and what can you complain of.
But I think "do everything machines" are necessarily inevitable but the situation does make it uncertain where the limits are.
In the exact same way that LLMs allow anyone to vibe code an app but do not replace real understanding of system design due to its essential complexity, non-mathematicians will quickly learn that asking an LLM to pump out advanced mathematical statements to you, even if they are correct (and even if you could verify them) does not constitute understanding, and that the human brain is the bottleneck either way.
It is only if the LLM is super-human at simplification and explaining that a difference will be noted. This would be excellent for mathematics but its not a foregone conclusion (and the argument of most mathematicians, such as Terence Tao, is that this distillation process is one of the key parts of doing mathematics, and that LLMs so far seem to be going in the opposite direction. I suspect its probably user error and leveraging the tools better will produce different outcomes, but mathematicians are only just starting the journey that software developers have been going through, so patience is needed).
Why should we expect everyone to be both a great researcher and communicator? The obvious result is that it is as effective as engineering managers. Sure, there's some amazing ones, but most aren't. Though that also doesn't mean no expertise in the field (i.e. non-engineering manager) is any better. It is just that managing/communicating is a different and orthogonal skill.
What needs to happen is we need to make it okay for people to specialize in more things. More nuance to this rather than trying to throw everyone into nice easy to manage buckets. Those buckets are just unrealistic abstractions filled with hope, denial, and laziness. Reality is surprisingly complex. Math can do a really good job helping you understand that, but it's a sufficient condition, not a necessary one
Not that I actually agree that math was at the right level of gatekeeping. It definitely feels intentionally opaque beyond reason, and I think it's why LLMs are able to cut through the obfuscation and solve problems that maybe wouldn't actually have been considered quite so hard if mathematicians did a better job of making their work accessible.
And, who said anything about Japan? Confused.
Result is more software at lower quality. The reason is statistics. When you increase the population, you increase the population of every kind of programmer, and people who want the result are favored in most competitive sectors because corporations want something somewhat working yesterday.
...and here we are.
Now programmers talking about code quality is stoned en-masse. If it's somewhat working then it's good. Efficiency, resiliency, maintainability and sustainability is an afterthought. Some of my friends who loved debating programming language theory now don't even care about the code. They don't write it, just vibe, and they don't plan to come back to "older, caveman style of development".
Some universities are also adding fuel to the fire: They "prepare students for the job", not teaching the science, but the parts that corporations need for the job only.
Though, hardware was cheap and people were expensive, and now code is cheap and hardware is expensive now. We'll see.
> we lost the joy of the journey and only fixated at the destination.
that's because you can make money with code and so it went the same way as everything else that's capitalized/commodified.
here a better comparison would be art which is generally still pursued on its own merits/pleasures.
When you look at older software, most of it was higher quality than the things we have today. A web site contained more information in a more readable way, more features in a smaller footprint. Same for native applications.
Now we slap what we found online together and calling it done. Everything is sparse, takes ages to load, centuries to submit and everything is so disconnected and async that some simple features are straight out impossible.
This is what fixating on the destination brought us. I dare you to download something you purchased 3 months ago via a 4096 character S3 link they have sent you, and double dare you to ask customer support for a new link. I'll bet that with a 80% chance they have no way to verify your serial number, even.
Somebody said that lowering the bar is not good. Somebody else asked for examples, and I provided an example. So, if you want to be pedantic, that doesn't track well, because what I answered was not about mathematics.
If you want something about mathematics, computation is mathematics, as software is. So, my example tracks the same way in mathematics.
Finding solutions without understanding its parts or the path is equally detrimental to mathematics as it is detrimental to software.
Maybe you need to read a bit slower and think along the way. Using AI too much blunts critical thinking skills in some, as I read.
What was the end of the proof thing you mathematicians use, was it "Q.E.D."?
Q.E.D.
brother i already addressed this literally in my first response to you: the reason software went to shit is because it became commodified (ie a thing produced in a factory) not because it's computational nor because the bar got lowered. seriously read my whole original reply again and see whether you really disagree before just re-asserting your rant on SWE.
> Finding solutions without understanding its parts or the path
you didn't read the post at all did you? it's emphatically about deep understanding over blind results.
> Using AI too much blunts critical thinking skills in some, as I read.
irony
What about the crafts? Carpentry, blacksmithing, stonesmithing, etc. are all commodified yet people still pursue these for pleasure.
>this comparison makes little sense.
Stop gatekeeping what people find personally fulfilling.
they're literaly not - do you know what the word artisanal means?
> Stop gatekeeping what people find personally fulfilling
wut? i can't even parse this in relation to what i wrote (which is that people who enjoy math will continue to be able to).
https://www.merriam-webster.com/dictionary/artisan
Do you?
>they're literaly not
Are you arguing that all the metal we have in our cars, buildings, airplanes is still being forged by hand? That that the furniture people are buying off Amazon is handmade? That stonework isn't primarily done these days with concrete pours?
>(which is that people who enjoy math will continue to be able to).
You posited that code is not like art, because it's primarily written for money and not for pleasure. But that's a stupid fucking argument, because there are plenty of crafts out there that are both done for money and pleasure (often by the same people!).
I agree making simple things sound complicated to appear more impressive is bad but there are limits. Even with Feynman he could only go so far, e.g. his interview about why questions and magnetism.
I do think in a lot of fields there is a lot of impact/influence to be had by people who are willing to do work to bridge different fields. I wonder to what degree this is because practitioners don't always see how their work could be used elsewhere.
Pedagogy is the primary purpose of educational institutions. That includes universities. However, when research is placed first, you are often left with mediocre teachers, because "who cares?" They were hired to do research and lend the university that kind of prestige; teaching is an afterthought squeezed into the spaces that remain.
And frankly, we haven't the faintest clue today what education is even for. That doesn't bode well.
Add to this the other troubles facing the university, like declining attendance, skyrocketing costs, and AI cheating and we're in for a very interesting transition indeed.