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The whole tirade on rigorous proofs and colonial mindset puzzles me. From my understanding (I am European ...), rigorous proofs were increasingly seen as a nee

The whole tirade on rigorous proofs and colonial mindset puzzles me. From my understanding (I am European ...), rigorous proofs were increasingly seen as a need because as things like calculus progressed, any loose definition had a tendency to become a minefield. Think of the definition of derivatives, continuity. Also, at a time where things were getting mechanize because we could and it was a gain, it was natural to check if we could somehow mechanize math. After all, Pascal made a machine that could do sums, why not a machine for proofs ?

thoi23u4234324 3y ago
I don't think 'colonial' is the right word; I think it's more to do with theology and Europe's very twisted (and ongoing) history with it. A very clear example is S Ramanujan's way of doing mathematics, where proofs were secondary to 'calculate, calculate, calculate, then hypothesize, then maybe prove' approach. This was not a one off thing, nor was his strange approach unique. Indian traditional mathematics also follows SR's approach of compute & then generalize & then prove (which most working mathematicians actually follow to some degree anyway). India was ahead of much of the world in Math until the cusp of renaissance(finally culminating in the dev. of calculus a good hundred years before Newton, and possibly having traveled to and 'inspired' him with the Jesuit missions), and its outcome's are simply extraordinary. Of course, the tradition was not given any credit whatsoever due to the prevalent racial-thinking in old-Europe; this now continues because Indologists continue to hold onto their inherited toxic racial thinking and prevent anyone else from touching this subject because 'Hindus are bad/dirty/nazis/<add adjective> people' (you see this with Yoga, NSDR, Mindfullness,... to this day). Regardless of all the 'credit allocation' business, and somewhat more importantly, it's actually really sad that this tradition is no longer alive, and is instead replaced with a cheap mimicry of Europe. C K Raju has written extensively on this. It's also not like this way of doing math. is inherently worse. A lot of actual formal math, starting from the construction of real-numbers is actually very 'unreal' when you get down to it. The kinds of hiccups thrown up by real-numbers in the theory of computation needs to be seen to be believed. Chaitin even has a paper by the title 'How real are real numbers'... We actually get around many of these weird issues because the construction of formal mathematics is actually based on ensuring that discretization is stable (this doesn't work in TOC). Still one also can't deny the strides that modern mathematics has made, in large part built on formalization. All said, to destroy any existing tradition (even Western) is extremely detestable. OTOH given that it is a jealous-monoculture (all of academia has become one big church-like monoculture at this point), the creation of a new tradition needs active support. I wish people would spend time on the latter instead of pointless race-wars (or DEI non-sense). (edit: expand)
nxobject 3y ago
I'm a little confused by your description – it doesn't seem like a tirade at all (and indeed "colonial" is the interviewer's phrase), or even a judgment on anything: more like a sober conversation about the history of mathematics, the introduction of proof, the role of the Western tradition, and what "mathematical thought" has looked like elsewhere. I might suggest we're seeing the word "colonialism" and jumping to assumptions. I think there's a quote that illustrates her argument more accurately: 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.
a_bonobo 3y ago
I've just finished reading Feyerabend's Tyranny of Science which goes down a very similar path to OP's interview: >In this wide-ranging and accessible book Feyerabend challenges some modern myths about science, including the myth that ‘science is successful’. He argues that some very basic assumptions about science are simply false and that substantial parts of scientific ideology were created on the basis of superficial generalizations that led to absurd misconceptions about the nature of human life. Far from solving the pressing problems of our age, such as war and poverty, scientific theorizing glorifies ephemeral generalities, at the cost of confronting the real particulars that make life meaningful. Objectivity and generality are based on abstraction, and as such, they come at a high price. For abstraction drives a wedge between our thoughts and our experience, resulting in the degeneration of both. Theoreticians, as opposed to practitioners, tend to impose a tyranny on the concepts they use, abstracting away from the subjective experience that makes life meaningful. Feyerabend concludes by arguing that practical experience is a better guide to reality than any theory, by itself, ever could be, and he stresses that there is no tyranny that cannot be resisted, even if it is exerted with the best possible intentions. In other words: there's a 'tacit knowledge' that we ignore by just writing down what we can measure in numbers. Feyerabend died before it became en vogue to talk about colonialism's impact, but his points are similar. (This ties in with her gut feeling: the scientific literature pretends the gut feeling does not exist, we invent a logical story of how we've deduced an insight after we've stumbled over the insight)
- marmakoide 3y ago
  The scientific literature pretending that gut feeling does not exist, is, in my own opinion, a legend. Most discoveries/invention were stumbled upon by collective efforts, a bit of intuition, lots of work, and a share of luck. Once something is found/made, then we clean up so as it can be shared and taught. Scientists always had gut feelings, routinely shared and share their feelings, it's what makes most of discussion between scientists. It was always ok to have feelings. However, to build something somewhat reliable, feelings are not enough, so you do the work to turn a feeling into a falsifiable theory that ypu put to the test.
  - 3y ago

thoi23u4234324 3y ago

I don't think 'colonial' is the right word; I think it's more to do with theology and Europe's very twisted (and ongoing) history with it. A very clear example is S Ramanujan's way of doing mathematics, where proofs were secondary to 'calculate, calculate, calculate, then hypothesize, then maybe prove' approach. This was not a one off thing, nor was his strange approach unique. Indian traditional mathematics also follows SR's approach of compute & then generalize & then prove (which most working mathematicians actually follow to some degree anyway). India was ahead of much of the world in Math until the cusp of renaissance(finally culminating in the dev. of calculus a good hundred years before Newton, and possibly having traveled to and 'inspired' him with the Jesuit missions), and its outcome's are simply extraordinary. Of course, the tradition was not given any credit whatsoever due to the prevalent racial-thinking in old-Europe; this now continues because Indologists continue to hold onto their inherited toxic racial thinking and prevent anyone else from touching this subject because 'Hindus are bad/dirty/nazis/<add adjective> people' (you see this with Yoga, NSDR, Mindfullness,... to this day). Regardless of all the 'credit allocation' business, and somewhat more importantly, it's actually really sad that this tradition is no longer alive, and is instead replaced with a cheap mimicry of Europe. C K Raju has written extensively on this. It's also not like this way of doing math. is inherently worse. A lot of actual formal math, starting from the construction of real-numbers is actually very 'unreal' when you get down to it. The kinds of hiccups thrown up by real-numbers in the theory of computation needs to be seen to be believed. Chaitin even has a paper by the title 'How real are real numbers'... We actually get around many of these weird issues because the construction of formal mathematics is actually based on ensuring that discretization is stable (this doesn't work in TOC). Still one also can't deny the strides that modern mathematics has made, in large part built on formalization. All said, to destroy any existing tradition (even Western) is extremely detestable. OTOH given that it is a jealous-monoculture (all of academia has become one big church-like monoculture at this point), the creation of a new tradition needs active support. I wish people would spend time on the latter instead of pointless race-wars (or DEI non-sense). (edit: expand)

nxobject 3y ago

I'm a little confused by your description – it doesn't seem like a tirade at all (and indeed "colonial" is the interviewer's phrase), or even a judgment on anything: more like a sober conversation about the history of mathematics, the introduction of proof, the role of the Western tradition, and what "mathematical thought" has looked like elsewhere. I might suggest we're seeing the word "colonialism" and jumping to assumptions. I think there's a quote that illustrates her argument more accurately: 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.

a_bonobo 3y ago

I've just finished reading Feyerabend's Tyranny of Science which goes down a very similar path to OP's interview: >In this wide-ranging and accessible book Feyerabend challenges some modern myths about science, including the myth that ‘science is successful’. He argues that some very basic assumptions about science are simply false and that substantial parts of scientific ideology were created on the basis of superficial generalizations that led to absurd misconceptions about the nature of human life. Far from solving the pressing problems of our age, such as war and poverty, scientific theorizing glorifies ephemeral generalities, at the cost of confronting the real particulars that make life meaningful. Objectivity and generality are based on abstraction, and as such, they come at a high price. For abstraction drives a wedge between our thoughts and our experience, resulting in the degeneration of both. Theoreticians, as opposed to practitioners, tend to impose a tyranny on the concepts they use, abstracting away from the subjective experience that makes life meaningful. Feyerabend concludes by arguing that practical experience is a better guide to reality than any theory, by itself, ever could be, and he stresses that there is no tyranny that cannot be resisted, even if it is exerted with the best possible intentions. In other words: there's a 'tacit knowledge' that we ignore by just writing down what we can measure in numbers. Feyerabend died before it became en vogue to talk about colonialism's impact, but his points are similar. (This ties in with her gut feeling: the scientific literature pretends the gut feeling does not exist, we invent a logical story of how we've deduced an insight after we've stumbled over the insight)

marmakoide 3y ago
The scientific literature pretending that gut feeling does not exist, is, in my own opinion, a legend. Most discoveries/invention were stumbled upon by collective efforts, a bit of intuition, lots of work, and a share of luck. Once something is found/made, then we clean up so as it can be shared and taught. Scientists always had gut feelings, routinely shared and share their feelings, it's what makes most of discussion between scientists. It was always ok to have feelings. However, to build something somewhat reliable, feelings are not enough, so you do the work to turn a feeling into a falsifiable theory that ypu put to the test.
- 3y ago