"Its ability to understand complex ideas is not limited by the ability of a single human brain to apprehend, intuit, or communicate those ideas." Incorrect. LLMs "understand" exactly nothing and there is nothing in their archtitecture that puts them on the path to doing so. The lack of an LLM's ability to perform abductive reasoning is why mathematicians are still every bit as important as they ever were. Giving a word processor credit for the original work of an author would be equivalent to giving the AIs credit for solving the theories developed by mathematicians.
Mathemticians are at the very pinnacle of human thought. They will be among the last to be replaced by AI and that will require that machines actually learn to think, not just appear to think.
I'll bring out my usual response to this kind of claim: What's the *least* impressive cognitive task that you believe LLMs will never be able to do because of this fundamental limitation?
I am a former mathematician and I meet maths students during regular Spring and Fall Schools of Algebra that my department holds.
The community is neither blasé nor as dismissive as you. For the usual standards of a specialization that usually insists on exact definitions, few waste their time on picking apart the meaning of "understand", not least because we don't really understand how our human cognition works and if it is indeed somehow superior to what LLMs do or not.
What matters to them is that this ... entity ... produces top-level mathematical results. The comparison to word processors is misleading. You cannot leave Libre Office running overnight and return to it with an expectation that there will be Hemingway-level prose on the screen.
The level of uncertainty among the young is now unprecedented - no one even tries to guess how the field will look five or ten years from now, but the general rule in the academia is that the old guard tries to protect its jobs and positions first and foremost, so any massive change will likely come at the cost of the new entrants.
“We motivate ourselves with our own sense of heroism, and to be reminded that we’re cogs in a machine greater than ourselves makes life seem a little less meaningful.”
It’s similar to how many religious people of yore thought that by seeking to understand the universe in scientific terms would strip all the wonder, meaning, and beauty from it…and, uh, nope. The universe described by science is awe inspiring, gorgeous, and fucking nuts!
I guess I’m saying that having better tools to go farther down the rabbit hole has always made the world more interesting and inspiring.
I really enjoyed the provocation around how heroism has to change, how we perhaps need a shift away from solely focusing on individual achievement
A lot of people are arguing that relationships will be the new binding constraint if individual knowledge is cheap and easy to come by. I think that lens is still highly individualistic - I think the binding constraint will be more about the output of complex collaborative efforts
Perhaps we are seeing the end of the creative potential of individualism. I worry though about the psychological effects - what comes to mind is the discussion around what the "enclosure of the frontier" meant psychologically for Americans, and how the economic reality of a continued ability to claim homestead land didn't really do enough to counteract the feelings that the US was losing something in the process.
Which is also why I like the focus here on heroism specifically - the stories we tell ourselves about what's happening at the "frontier" are quite important
"Its ability to understand complex ideas is not limited by the ability of a single human brain to apprehend, intuit, or communicate those ideas." Incorrect. LLMs "understand" exactly nothing and there is nothing in their archtitecture that puts them on the path to doing so. The lack of an LLM's ability to perform abductive reasoning is why mathematicians are still every bit as important as they ever were. Giving a word processor credit for the original work of an author would be equivalent to giving the AIs credit for solving the theories developed by mathematicians.
Mathemticians are at the very pinnacle of human thought. They will be among the last to be replaced by AI and that will require that machines actually learn to think, not just appear to think.
I'll bring out my usual response to this kind of claim: What's the *least* impressive cognitive task that you believe LLMs will never be able to do because of this fundamental limitation?
I am a former mathematician and I meet maths students during regular Spring and Fall Schools of Algebra that my department holds.
The community is neither blasé nor as dismissive as you. For the usual standards of a specialization that usually insists on exact definitions, few waste their time on picking apart the meaning of "understand", not least because we don't really understand how our human cognition works and if it is indeed somehow superior to what LLMs do or not.
What matters to them is that this ... entity ... produces top-level mathematical results. The comparison to word processors is misleading. You cannot leave Libre Office running overnight and return to it with an expectation that there will be Hemingway-level prose on the screen.
The level of uncertainty among the young is now unprecedented - no one even tries to guess how the field will look five or ten years from now, but the general rule in the academia is that the old guard tries to protect its jobs and positions first and foremost, so any massive change will likely come at the cost of the new entrants.
“We motivate ourselves with our own sense of heroism, and to be reminded that we’re cogs in a machine greater than ourselves makes life seem a little less meaningful.”
It’s similar to how many religious people of yore thought that by seeking to understand the universe in scientific terms would strip all the wonder, meaning, and beauty from it…and, uh, nope. The universe described by science is awe inspiring, gorgeous, and fucking nuts!
I guess I’m saying that having better tools to go farther down the rabbit hole has always made the world more interesting and inspiring.
The sheer naivete of saying that mathematics as a profession will be fine because it only costs 5-6 billion dollars is wild.
Lots of academic fields cost far less and are nevertheless being destroyed anyway.
Lovely post. One correction: Wiles was less than a decade before Perelman, not a generation before.
Andrew Wiles completed his proof of Fermat's Last Theorem in 1994. Grigori Perelman proved the Poincaré conjecture in 2002–2003.
It's also interesting that Perelman himself very much disagreed with the idea Noah expresses here, that his own contribution carried a special status.
I really enjoyed the provocation around how heroism has to change, how we perhaps need a shift away from solely focusing on individual achievement
A lot of people are arguing that relationships will be the new binding constraint if individual knowledge is cheap and easy to come by. I think that lens is still highly individualistic - I think the binding constraint will be more about the output of complex collaborative efforts
Perhaps we are seeing the end of the creative potential of individualism. I worry though about the psychological effects - what comes to mind is the discussion around what the "enclosure of the frontier" meant psychologically for Americans, and how the economic reality of a continued ability to claim homestead land didn't really do enough to counteract the feelings that the US was losing something in the process.
Which is also why I like the focus here on heroism specifically - the stories we tell ourselves about what's happening at the "frontier" are quite important
Wide reflection. Notably the last three paragraphs.