5 ms·

I appreciated Eugenia Cheng's youtube lectures on category theory and I know interviews aren't the best format for sustained exposition, but the remark about ma

I appreciated Eugenia Cheng's youtube lectures on category theory and I know interviews aren't the best format for sustained exposition, but the remark about mathematical rigor being a European colonialist thing seemed pretty forced. If anything, it underestimates the strangeness of the history of math in an effort to cram it into a simple frame: "Europeans bad". There was something distinctive about work in foundations of math in the late 19th / early 20th centuries, work which came out of European cultures (or more accurately Latin Christendom). Plausibly, this work was centuries in the making, the culmination of a trend towards increasingly analytic and systematizing modes of thought that begins with the recovery of Greek philosophy in the middle ages. But, ok, even if you don't buy that, how do you get from the Congo Free State to Frege, Hilbert and Goedel? It's a radical claim that would be utterly fascinating if it were true. But Chang just kind of tosses it off at the end and asks us to accept it as an unremarkable truism.

nxobject 3y ago
I've talked about this in a replay to another comment, but I don't think she's making any value judgment in the article, or (at least in the article) actually articulating any claim about colonialism and mathematics. In fact, I don't even think she's saying "Europeans bad": We might marvel at, say, Amish people raising a barn or Inuit people building a kayak without any European formal maths training. We might declare that this is maths — and I think it is. But it’s problematic if we think we’re doing them some great honour by bestowing the label of maths on what they do.
- lambdaphagy 3y ago
  I think that if I were being interviewed and my interviewer said "you also discuss how colonialist ideology has influenced modern mathematics?", but I didn't think that colonialist ideology has influenced modern mathematics, I would say: "What? I don't think colonialist ideology has influenced modern mathematics at all." Rather than insinuating that Europe must have stolen math from other parts of the world and pawned it off as its own, or been really mean about rigor, or whatever. There were several totalizing ideologies in the 20th century that attempted to make all of human affairs about themselves: everything from literature to science to birdwatching had some sort of party line: Did this literature say the right things? Was this science done by the right kind of scientist? Is this bird the right kind of bird to be watching? Judging by their results, I wouldn't look forward to a do-over of that line of thinking.
  - nxobject 3y ago
    I think that's our disagreement: I think you can say, "maybe there's some relationship between what we have seen as colonialism and academic mathematics", without even thinking that it was about "stealing math", or thinking about colonialism determined everything about mathematics in some totalizing way. I'm sorry if I come off as a little obtuse, so I might as well say what I'm really thinking. My thinking leans towards Eugenia's, and it's a lot more conservative: the question itself is worth thinking about, but it's a lot to think through, and the link may as well be tenuous. But, in my thinking, if NATO once funded pure mathematics (as Grothendieck once protested against), if DARPA also currently funds pure mathematics, then it is worth asking what historical narrative explains it, and whether it applies to the slightly more distant past, too. Above all I don't believe that the academic enterprise has ever been a neutral and disinterested endeavor, either – it's a lot of public money, and wherever there's public money politics comes before or after. I don't think that's a totalizing way of understanding academia.
    - lambdaphagy 3y ago
      Cheng talks a lot about colonialism inn _Is Maths Real_ but here is the closest thing to an argument for the claim that I could locate: > “Now, at the same time as all this, it is true that mathematics as a field has grown carefully and rigorously according to a carefully constructed framework of logic and rigour. It is, arguably, the framework that is keeping some maths in and keeping some maths out. But... there are questions about the values built into the framework of mathematics. That framework is geared towards the principles of ‘progress’ and ‘development’. Deep down I have an uncomfortable suspicion that those principles are indelibly linked to colonialism, imperialism and the urge to conquer others.” (p. 320-1) That's the argument in its entirety. What humanity was up to in the ten millennia of recorded history before formal mathematics is left unexplained. The most parsimonious explanation for the military's funding of mathematics research is that mathematics often has applications to military technology. But even here, we have to be careful: it's typically applied math that's the most, well... applicable, which is precisely the sort of thing that pure mathematicians are supposed to look down upon as "not really math". (The pure math work at DARPA is AFAICT more a consequence of DARPA's idiosyncratic governance structure that gives program managers wide latitude to swing for the fences, accepting that there will be some strikeouts.) But the fact that modern Western mathematics is indispensable for advanced engineering projects at all, in a way that Sanskrit prosody and Inuit kayak architecture are not, is pretty crucial to understanding the funding situation: it's funded because it's useful, not useful because it's funded. If we don't grant that math is actually unreasonably effective in explaining / predicting / manipulating the world then sure, what math gets funded looks like another courtly intrigue. But it seems that the unreasonable effectiveness is precisely what needs to be explained away on Cheng's view. I'm all ears for the contrary view, but we've already written more on the topic than Cheng did in the entire book, which is light on argument and regrettably heavy on insinuation.

nxobject 3y ago

I've talked about this in a replay to another comment, but I don't think she's making any value judgment in the article, or (at least in the article) actually articulating any claim about colonialism and mathematics. In fact, I don't even think she's saying "Europeans bad": We might marvel at, say, Amish people raising a barn or Inuit people building a kayak without any European formal maths training. We might declare that this is maths — and I think it is. But it’s problematic if we think we’re doing them some great honour by bestowing the label of maths on what they do.

lambdaphagy 3y ago
I think that if I were being interviewed and my interviewer said "you also discuss how colonialist ideology has influenced modern mathematics?", but I didn't think that colonialist ideology has influenced modern mathematics, I would say: "What? I don't think colonialist ideology has influenced modern mathematics at all." Rather than insinuating that Europe must have stolen math from other parts of the world and pawned it off as its own, or been really mean about rigor, or whatever. There were several totalizing ideologies in the 20th century that attempted to make all of human affairs about themselves: everything from literature to science to birdwatching had some sort of party line: Did this literature say the right things? Was this science done by the right kind of scientist? Is this bird the right kind of bird to be watching? Judging by their results, I wouldn't look forward to a do-over of that line of thinking.
- nxobject 3y ago
  I think that's our disagreement: I think you can say, "maybe there's some relationship between what we have seen as colonialism and academic mathematics", without even thinking that it was about "stealing math", or thinking about colonialism determined everything about mathematics in some totalizing way. I'm sorry if I come off as a little obtuse, so I might as well say what I'm really thinking. My thinking leans towards Eugenia's, and it's a lot more conservative: the question itself is worth thinking about, but it's a lot to think through, and the link may as well be tenuous. But, in my thinking, if NATO once funded pure mathematics (as Grothendieck once protested against), if DARPA also currently funds pure mathematics, then it is worth asking what historical narrative explains it, and whether it applies to the slightly more distant past, too. Above all I don't believe that the academic enterprise has ever been a neutral and disinterested endeavor, either – it's a lot of public money, and wherever there's public money politics comes before or after. I don't think that's a totalizing way of understanding academia.
  - lambdaphagy 3y ago
    Cheng talks a lot about colonialism inn _Is Maths Real_ but here is the closest thing to an argument for the claim that I could locate: > “Now, at the same time as all this, it is true that mathematics as a field has grown carefully and rigorously according to a carefully constructed framework of logic and rigour. It is, arguably, the framework that is keeping some maths in and keeping some maths out. But... there are questions about the values built into the framework of mathematics. That framework is geared towards the principles of ‘progress’ and ‘development’. Deep down I have an uncomfortable suspicion that those principles are indelibly linked to colonialism, imperialism and the urge to conquer others.” (p. 320-1) That's the argument in its entirety. What humanity was up to in the ten millennia of recorded history before formal mathematics is left unexplained. The most parsimonious explanation for the military's funding of mathematics research is that mathematics often has applications to military technology. But even here, we have to be careful: it's typically applied math that's the most, well... applicable, which is precisely the sort of thing that pure mathematicians are supposed to look down upon as "not really math". (The pure math work at DARPA is AFAICT more a consequence of DARPA's idiosyncratic governance structure that gives program managers wide latitude to swing for the fences, accepting that there will be some strikeouts.) But the fact that modern Western mathematics is indispensable for advanced engineering projects at all, in a way that Sanskrit prosody and Inuit kayak architecture are not, is pretty crucial to understanding the funding situation: it's funded because it's useful, not useful because it's funded. If we don't grant that math is actually unreasonably effective in explaining / predicting / manipulating the world then sure, what math gets funded looks like another courtly intrigue. But it seems that the unreasonable effectiveness is precisely what needs to be explained away on Cheng's view. I'm all ears for the contrary view, but we've already written more on the topic than Cheng did in the entire book, which is light on argument and regrettably heavy on insinuation.