It is a strong argument in this case though, because Terence Taos expertise is directly linked to his ability to not misstate the history of mathematics.
Also note how the quote by Tao is in all likelyhood not meant as an absolute; rather than a statement of a trend - a handfull of counterexamples do I no way change anything about the truth value of Tao's quote.
On the other heand; consider how absurd it would be if "... in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science ..." would indeed be a misstatement; which would imply that far more promising research directions were not shared with the broader community (i.e.: published). I wonder what different reading of that counterfactual there could be other than secret societies that kept their discoveries and research directions to themselves - which we just learned about (since we would otherwise not be refering to the secret societies and their supposed promising research directions).
All pretty straightforward, I would say - both that "misstatement" is hopefully based an overly strict reading of Tao's quote, and that mentioning Tao's background as one of the fields leading practitioners is relevant as well. Again; to make sure: A few counterexamples achieves nothing here. It would need to reach a certain threshold of such counterexamples before we will have to write the history of mathematics; and before Tao actually made a misstatement here.
I mean mathematics has enough history that something can both have been false for centuries of mathematics research and true for centuries. Sometimes in different places simultaneously.
Terrence Tao can do his job perfectly well without being aware of any mathematical history, though I consider it unlikely that he is. I'm not seeing the direct link you're talking about, in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts.
And the other an appeal to tradition. There was only one Gauss to scoop and focusing on him misses the larger math culture which Terry might be aware of, where most trust others to not scoop.
And if any mathematician's AI usage on a problem leads to scooping, the volume of agents involved gives them a huge advantage which could prompt mathematicians to not use LLMs.
Though you can say Terry's claim is a slippery slope.
So let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority?
Knowing the math that was developed through history, and knowing how that math was developed and the circumstances around it are two fundamentally different things.
Clearly Tao knows the former, but apriori that does not imply he knows the latter.
Not saying he doesn't, just saying one does not imply the other.
Even if you go back and read the original papers, you'll miss all that which happened beyond the page.
> Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history?
If Tao has a knowledge of the topic (which he does), then it isn't by virtue of being a mathematician per se, but by virtue of an interest in the history of mathematics (which he has). Knowledge of math is enormously helpful here, but it does not imply historical knowledge.
Do you have a real argument to make rather than just appealing to authority?
It is a strong argument in this case though, because Terence Taos expertise is directly linked to his ability to not misstate the history of mathematics.
Also note how the quote by Tao is in all likelyhood not meant as an absolute; rather than a statement of a trend - a handfull of counterexamples do I no way change anything about the truth value of Tao's quote.
On the other heand; consider how absurd it would be if "... in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science ..." would indeed be a misstatement; which would imply that far more promising research directions were not shared with the broader community (i.e.: published). I wonder what different reading of that counterfactual there could be other than secret societies that kept their discoveries and research directions to themselves - which we just learned about (since we would otherwise not be refering to the secret societies and their supposed promising research directions).
All pretty straightforward, I would say - both that "misstatement" is hopefully based an overly strict reading of Tao's quote, and that mentioning Tao's background as one of the fields leading practitioners is relevant as well. Again; to make sure: A few counterexamples achieves nothing here. It would need to reach a certain threshold of such counterexamples before we will have to write the history of mathematics; and before Tao actually made a misstatement here.
I mean mathematics has enough history that something can both have been false for centuries of mathematics research and true for centuries. Sometimes in different places simultaneously.
Terrence Tao can do his job perfectly well without being aware of any mathematical history, though I consider it unlikely that he is. I'm not seeing the direct link you're talking about, in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts.
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And the other an appeal to tradition. There was only one Gauss to scoop and focusing on him misses the larger math culture which Terry might be aware of, where most trust others to not scoop.
And if any mathematician's AI usage on a problem leads to scooping, the volume of agents involved gives them a huge advantage which could prompt mathematicians to not use LLMs.
Though you can say Terry's claim is a slippery slope.
So let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority?
Get outta here.
Soldiers rarely know the history of war, and war historians are rarely soldiers.
1 reply →
Knowing the math that was developed through history, and knowing how that math was developed and the circumstances around it are two fundamentally different things.
Clearly Tao knows the former, but apriori that does not imply he knows the latter.
Not saying he doesn't, just saying one does not imply the other.
Even if you go back and read the original papers, you'll miss all that which happened beyond the page.
> Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history?
If Tao has a knowledge of the topic (which he does), then it isn't by virtue of being a mathematician per se, but by virtue of an interest in the history of mathematics (which he has). Knowledge of math is enormously helpful here, but it does not imply historical knowledge.
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