

What are you doing now? I feel like after I graduate I’m gonna have to find a new field.


What are you doing now? I feel like after I graduate I’m gonna have to find a new field.


If it’s actually exploiting a bug in a formal system, no. If it’s a natural-language (unformalized) document which no one can understand, no. On the other hand a formal proof not using bugs which can’t be understood, is still considered a proof, though its value is lower than an understandable proof (because as you said in another comment, the real value is in understanding rather than theorems). The prototypical example before LLMs was the proof of the four-color theorem which relied on computer-checked casework.


If the growth is superexponential, we make it so that each successive doubling takes 10% less time.
(From AI 2027, as quoted by titotal.)
This is an incredibly silly sentence and is certainly enough to determine the output of the entire model on its own. It necessarily implies that the predicted value becomes infinite in a finite amount of time, disregarding almost all other features of how it is calculated.
To elaborate, suppose we take as our “base model” any function f which has the property that lim_{t → ∞} f(t) = ∞. Now I define the concept of “super-f” function by saying that each subsequent block of “virtual time” as seen by f, takes 10% less “real time” than the last. This will give us a function like g(t) = f(-log(1 - t)), obtained by inverting the exponential rate of convergence of a geometric series. Then g has a vertical asymptote to infinity regardless of what the function f is, simply because we have compressed an infinite amount of “virtual time” into a finite amount of “real time”.
No, it was literally an asymptote.