waynecochran

I would really like to see an AI invent a new set of (consistent) axioms from which a whole slew of new problems and solutions arise. Something akin to Euclidean geometry, but for a whole new landscape of theorems.

LEAN and other tools verify from what do know -- at least stepwise. Anything that deviates from these things should stick out. I suppose some million line LEAN program may have embedded within it something that is novel and not readily apparent, but I imagine truly novel approaches should stick out like a sore thumb.

Could AI create a novel set of axioms (a new math) from which things like RH become a by product? I think that would be hard to miss.

What is the current thought on AI creating new emergent forms of mathematics? Even the most stunning results like the proof of the quasi-RH are a clever combination of known mathematics. Humans have created (discovered?) stunning new ideas (e.g. complex numbers) that have opened wide new horizons -- do we think AI will be capable of creting / discovering novel new things like this?

Great. Glad it worked for you.

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.

<unbearable web page to read>

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.

Yes, it is hard, psychologically, to grant trust to some silly perverse little thing I want crush like a surreal cartoonish cockroach.

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.

My premise was that the proof was opaque -- i.e., no insight was to be gained from it.

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.

Fight fire w fire. Have AI read it and decide what to do w it.

Yes

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.

Apple and Jony Ive killed skeuomorph design a long time ago.

You do realize EV’s pollute as well? Batteries are nasty.

| The gas detected in the atmosphere is helium

The planet must have an enormous escape velocity to contain helium in its atmosphere. If there is life there they are stuck.

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.

It will be easier than trying to learn to the new features of C++34.

I think you misunderstand -- I am still reading the article.

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.