Comment by Animats
17 hours ago
"We’re gonna need a lot more mathematicians."
What the article really says is that we're going to need much smarter mathematicians. That is not possible for puny meat-brain humans. Humans are close to their ceiling. AIs are just getting started.
In practice, we're probably going to hit that limit first in IC design. I once went to a talk by the Intel engineering manager who headed the Pentium Pro effort. That was the first superscalar x86 CPU, and it took about 5,000 engineers at peak to design it. Getting that many people coordinated on one thing was a real achievement. Then Intel stayed with minor tweaks on that design for years.
We're soon going to be seeing designs of even greater complexity cranked out by AIs. No human will understand them at the gate level. Reading AI-written programming language code is bad enough. Reading AI-written Verilog may be beyond human comprehension, except in small sections.
> Humans are close to their ceiling. AIs are just getting started.
The whole point of mathematics is to vastly exceed that natural ceiling by gradually building a framework for understanding. In fact it’s wrong to speak of a ceiling altogether. If there were a ceiling, we’d have hit it long ago.
AIs have already swallowed the entire history of human thought, but apparently they’re ’just getting started’. I can only assume you don’t know what mathematicians actually do.
Abstractions can certainly enable this kind of "telescoping" effect of understanding, but not everything can be compressed with clever abstractions. Some things are inherently incompressible and there is no neat and insightful short explanation for why it is true, just a massive proof, but it may still have provably good properties for building a chip or power plant.
We have naturally only explored the mathematical universe in the parts where telescoping via clever abstractions can get us. But there is much more. Being able to juggle more things in your mind at the same time can have qualitatively massive benefits.
Information theory and proof theory, algorithmic information theory etc has of course explored this.
5000 engineers for the Pentium Pro?? Bob Colwell, chief architect of the Pentium Pro, says 450+ people with over 400 design and validation engineers. Source: "The Pentium Chronicles", pages xvi and 2.
> Humans are close to their ceiling.
If Math Academy teach 10 year old kids calculus, I doubt that.
Rule based Mechanics of taking derivatives and finding intervals is quite different from understanding delta epsilon proofs. I have no doubt 10 year old can do the former quite easily, the proofs on the other hand? Depends what you mean by “teaching calculus”!
> Humans are close to their ceiling.
Hopping on this train: the human ceiling 100 years ago is now advanced undergrad material in mathematics. I see no particular reason for this to change, especially with everyone in the math research pipeline pushing to compress the difference just as always before.
> I once went to a talk by the Intel engineering manager who headed the Pentium Pro effort. That was the first superscalar x86 CPU
The original Pentium was already superscalar, with its asymmetrical U and V pipes.
The Pentium Pro added out of order execution via register renaming. A true achievement, indeed.
And as for the more general point you are making: computer chips have been far too complex for any single human to comprehend for decades. I left NVidia after working there as an archutect for five years, barely understanding anything about those behemoths.
[dead]