Comment by contravariant
13 hours ago
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.
> in fact history is frequently left out of mathematical teaching even when the history would in fact help in the understanding of some concepts.
That is well-known I assumed and continue to assume.
> I'm not seeing the direct link you're talking about
You are stating that link yourself; indirectly: "though I consider it unlikely that he is [being unaware of any mathematical history]". Why is it unlikely, precisely?
- Maybe because it is unlikely that he recieved the mathematical teaching that frequently does not contain history of mathematics (wild! I wonder which university you have in mind in particular) that you seem to be refering to?
- Maybe because his writing is evidence that he is interested about, incorporates and refers to history of mathematics, refer for example to https://terrytao.wordpress.com/2008/01/04/pcm-article-genera... or https://terrytao.wordpress.com/career-advice/theres-more-to-...
- Or maybe because he is quite the opposite of a person that never ventures outside of their own area; being blind for other fields, or ones own history; as evidence by being famously collaborative across different fields, having a popular blog where he writes about non-mathematical topics too and last; him being one of the main proponents of foundational topics such as formalization of mathematics; or the use of LLMs for mathematical research.
Does all that really make it more likely to you that Tao is not aware of the existence of counterexamples like those the commenter above mentioned - more likely than the commenter simply having missed a nuance or taking something out of context?
If so; I would be genuinely curious why - people work differently, and I am always happy to learn, or close gaps in my own understanding.
Any one of the arguments you make here is already stronger than the original one. The problems with appeals to authority isn't that they are always false, it's that they are not a good argument.
And you say his "expertise is directly linked to his ability to not misstate the history of mathematics". And frankly, I disagree. If he happened to be misguided or even outright wrong about some parts of mathematical history I wouldn't think any less of him, nor do I think it matters much for the work he's actually paid to do. At worst it would result in an online discussion, which is arguably a good outcome not a bad outcome.