FORTRAN 77 was the language for the first programming language course I took. I absolutely hated computers and programming after that course. Later I took CS courses and used Pascal -- one day the concept of abstraction hit me as we were developing data structs in the 2nd semester and the light went on. That is when I first started to love programming. FORTRAN was thereafter referred to as the F language. Sorry to be a bummer, but I still recoil when I hear about that language.
I had to quit using desktop Safari because it essentially quit working. The problem had something to do with icloud. Apple assumes everyone is using icloud I imagine and does not handle corner cases for folks with full icloud disks or improper setups. I have an paid icloud subscription now, but I haven't looked back.
Yes, of course. It makes complete sense to have the implementation of a C++ compiler to be written in a highly portable and much simpler language like C.
Excellent description. I feel like I understand how a fridge works now -- when I took physics as a freshman in 1985 I was just surviving and I remember just getting it enough to pass the test on the thermo section but never really grasping it. You basically have a year to understand what it took man centuries to figure out.
I am not sure this is either end. An obscure proof to RH or P < NP does not seem to solve anything -- seems to leave us right where we are -- that was my point. We would know a fact for which we could do nothing with nor gain any new insight.
Would it matter if AI had a proof for RH or P < NP, but the proof was 1000 pages long that Leaf could verify but otherwise impenetrable by a human mind? We generally assume these are true already -- I am not sure a long convoluted proof puts us in a much different place.
Again with the gatekeeping. An AI generating a convoluted proof for some conjecture is not gatekeeping. It just does not care if you understand. It only cares enough that it can be verified -- usually using some other opaque proof tool like Lean.
Folks keep using the word "gate keeping" -- I never used that term nor implied intentional gate keeping. It's simply not caring if those outside the club understand -- there is no one guarding the door its just folks don't care if anyone finds it.
I am not thinking of intentional gatekeeping, but more of the kind where mathematicians build themselves their own island of concepts and notation with no thought of building a passageway for others to engage and make use of the theory.
I would find modern algebraic geometry highly useful as someone who works in computer graphics and computer vision, but much of the theory is akin to learning a new language and I don't get the sense that those who publish their work in this field care if I enter their world.
It is not lowering the bar to find better ways to demystify and explain things. In fact, I would say those who can explain it well understand it the best. Richard Feynman would be my best example.
As someone who has a degree in math, I still can't help but think mathematicians are getting a little bit of a comeuppance. In a lot of areas of mathematics there had been little effort to make the work understandable and leaves numerous folks who could benefit from the knowledge on the outside looking in. Now AI comes along and do the same to mathematicians. Makes me chuckle a little bit.
LLM's may have provided a bit of comeuppance. Many mathematicians have cared little if anyone understands their obscure nomenclature and build mote around their work. Now they have encountered something that is becoming far more capable than they are and they may soon be left in the dark.
I am shipping sophisticated computer vision code that is more reliable and better tested than ever before. This isn't some vibe coded bullsh*t. This is me writing detailed mathematical specs and it do all the heavy lifting.
There has been a steady decline for decades. Release early, release often. One example: Apple used to have a thing called Gold Master release when updating software was not as immediate. The GM programs met a high bar for quality. Not so much anymore… the attitude is we can just release a new version later this week. There also used to be a thing called backwards compatibility… now no one thinks twice about breaking code on older platforms.
That is exactly what I was thinking. I was a seasoned C++ programmer and always loved reading articles like this. I can't imagine I will every write my own C++ code again -- or in any language. I now program with English specifications now and I am 10000% times more productive.
The main iPhone app I maintain for work is 100% claude edited now ... I don't touch the code anymore ... I do occasionally look at it. It does a way better job than I could. I do have Xcode open as claude does its thing ... and I occasionally sign and deploy with Xcode. No coding though.
That is the part Claude can handle and actually does. In fact, recently claude automaticaly converted some spline generating code to double precision and did some other refactoring as well after it realized poor results thru tests it generated on its own! I was gobsmacked!
... I believe many programmers at this point have less impact they could have because they look at the code.
I think my strength is now more in my ability as a mathematician and a writer than as a programmer. Being able to write detailed specs and doing QA by testing is far more productive than looking at code.
I am sure it probably was - a bit heavier option. There other mobile / VR / XR apps that I had to port to a variety of platforms using languages like Swift and Kotlin -- each platform has its own vector library. These don't necessarily provide SVD routines. Apple has their Accelerate framework, but is very unnatural to use IMO -- and Swift and C++ don't play that well together regardless of what folks say (that is why I tend to still use Obj-C++ when I have a choice).
There was another app where I had a 3x3 shear transformation that I needed to decompose into a rotation * scale * rotation which is exactly what SVD does (see https://tinyurl.com/384mkdvh). No need to bring in a full linear algebra package just for that.