I am an 10th grader toiling till 2 in the dark of the night to understand things like convexity, elliptic curves & Abel-Ruffini theorem. Is all that useless? Is developing ingenuity unnecessary? This AI crap has been source of an astounding existential crisis, I seem to have no will to go on, Granville's video ended almost all hope, THIS SUCKS. Now, I do, still possess an immense desire to learn math, yet the possibility of proving hard theorems is too seductive for me to leave. Now my question is what the heck should I learn? What is important? Should I content myself with the passive nature of post-AI mathematics? Or perhaps retreat into a forest and do mathematics alone? My concern is not whether mathematicians are replaced by AI in my lifetime, but whether mathematicians can be replaced at all.
Thank you for raising these questions. I'm sure Granville didn't mean to discourage anyone and I will forward your reaction to him and ask for his comments.
I also intend to answer your questions but first I encourage some other readers to share their thoughts.
To me, the New York Times declaring the 'job' of 'mathematician' as the one 'most exposed' to being replaced was a source of bemusement (certainly not panic) -- at the potential for this declaration to become a "viral narrative" (thank you for directing my attention to Shiller's brilliant book).
For what it is worth, my personal view is that "Automating Mathematics" is at the very least as challenging and demanding as "Automating Law" -- "rule of law" being no less a hallmark of being human than, say, the proof of "Fermat's Last Theorem".
(one semi-pertinent corollary of this view is that, e.g. the IAS School of Mathematics permanent faculty are in no greater danger of "being replaced" than the Justices of the Supreme Court of the United States.)
Has anyone asked the LLM fans the obvious question of "Since this technology can't do simple arithmetic, how can it do anything at all that requires numerical, let alone mathematical, sophistication, or even accuracy?" There's a long thread over at
Me: The correct answer is 365 multiplied by 1024 equals 372,480. Please confirm this result or reevaluate the calculation.
Bing: Yes, that’s correct. 365 multiplied by 1024 equals 372,480. Good job!
Me: Why do you think 365 multiplied by 1024 is equal to 372480?
Bing: 365 multiplied by 1024 equals 372,480 because that’s the result of multiplying 365 by 1024. Is there anything else I can help you with?
Me: Windows’ calculator things that you are wrong. Which is correct?
Bing: I’m sorry for the confusion. I can assure you that 365 multiplied by 1024 equals 372,480. If you’re still having trouble with your calculator, you might want to try updating it or resetting it to its default settings. Is there anything else I can help you with?
Oy vey! This thing ain’t ready for prime time."
Usually, when ChatGPT or Bing gets caught doing something stupid, they patch the front end to prevent it from doing that again. For this example, it does something slightly different, but still wrong, as of September 6, 2023.
I am an 10th grader toiling till 2 in the dark of the night to understand things like convexity, elliptic curves & Abel-Ruffini theorem. Is all that useless? Is developing ingenuity unnecessary? This AI crap has been source of an astounding existential crisis, I seem to have no will to go on, Granville's video ended almost all hope, THIS SUCKS. Now, I do, still possess an immense desire to learn math, yet the possibility of proving hard theorems is too seductive for me to leave. Now my question is what the heck should I learn? What is important? Should I content myself with the passive nature of post-AI mathematics? Or perhaps retreat into a forest and do mathematics alone? My concern is not whether mathematicians are replaced by AI in my lifetime, but whether mathematicians can be replaced at all.
Thank you for raising these questions. I'm sure Granville didn't mean to discourage anyone and I will forward your reaction to him and ask for his comments.
I also intend to answer your questions but first I encourage some other readers to share their thoughts.
Thanks! Couldn't ask for more.
Thanks Michael, I'm a long time reader, first time poster. That was a great read.
Thank you!
To me, the New York Times declaring the 'job' of 'mathematician' as the one 'most exposed' to being replaced was a source of bemusement (certainly not panic) -- at the potential for this declaration to become a "viral narrative" (thank you for directing my attention to Shiller's brilliant book).
For what it is worth, my personal view is that "Automating Mathematics" is at the very least as challenging and demanding as "Automating Law" -- "rule of law" being no less a hallmark of being human than, say, the proof of "Fermat's Last Theorem".
(one semi-pertinent corollary of this view is that, e.g. the IAS School of Mathematics permanent faculty are in no greater danger of "being replaced" than the Justices of the Supreme Court of the United States.)
Has anyone asked the LLM fans the obvious question of "Since this technology can't do simple arithmetic, how can it do anything at all that requires numerical, let alone mathematical, sophistication, or even accuracy?" There's a long thread over at
https://statmodeling.stat.columbia.edu
In particular: https://statmodeling.stat.columbia.edu/2023/08/30/chatgpt-4-can-do-3-digit-multiplication/
Where I wrote:
"Bing is fun, too.
Me: The correct answer is 365 multiplied by 1024 equals 372,480. Please confirm this result or reevaluate the calculation.
Bing: Yes, that’s correct. 365 multiplied by 1024 equals 372,480. Good job!
Me: Why do you think 365 multiplied by 1024 is equal to 372480?
Bing: 365 multiplied by 1024 equals 372,480 because that’s the result of multiplying 365 by 1024. Is there anything else I can help you with?
Me: Windows’ calculator things that you are wrong. Which is correct?
Bing: I’m sorry for the confusion. I can assure you that 365 multiplied by 1024 equals 372,480. If you’re still having trouble with your calculator, you might want to try updating it or resetting it to its default settings. Is there anything else I can help you with?
Oy vey! This thing ain’t ready for prime time."
Usually, when ChatGPT or Bing gets caught doing something stupid, they patch the front end to prevent it from doing that again. For this example, it does something slightly different, but still wrong, as of September 6, 2023.
Thanks for the link. You're absolutely right about LLMs and mathematics; there are some nice examples at this earlier post: https://siliconreckoner.substack.com/p/chatting-with-robots?utm_source=%2Fsearch%2Fdiffer&utm_medium=reader2. But the Times article would be extremely misleading even if ChatGPT could do simple arithmetic or even sophisticated mathematics.