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I was searching for information in a response to the OP in the following thread Foundational Mathematics:
https://www.physicsforums.com/threads/foundational-mathematics.1008334/
One of the recommended articles that popped up is William P. Thurston, "On Proof and Progress in Mathematics", Bulletin of the American Mathematical Society, Volume 30, Number 2, April 1994, pp. 161-177, which was written in response to an article by Arthur Jaffe and Frank Quinn, "Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physics," Bulletin of the American Mathematical Society, Volume 29, Number 1, July 1993, Pages 1-13. Reading Thurston's article prompted me to read the article by Jaffe and Quinn. It will take some time.
Thurston - https://arxiv.org/pdf/math/9404236.pdf
Jaffe and Quinn - https://arxiv.org/pdf/math/9307227.pdf
Of Jaffe and Quinn, Thurston writes the "article raises interesting issues that mathematicians should pay more attention to, but it also perpetuates some widely held beliefs and attitudes that need to be questioned and examined.
The article had one paragraph portraying some of my work in a way that diverges from my experience, and it also diverges from the observations of people in the field whom I’ve discussed it with as a reality check.
After some reflection, it seemed to me that what Jaffe and Quinn wrote was an example of the phenomenon that people see what they are tuned to see. Their portrayal of my work resulted from projecting the sociology of mathematics onto a one-dimensional scale (speculation versus rigor) that ignores many basic phenomena."
Thurston asks more or less, "What does one do as a mathematician?" He actually poses, "How do mathematicians advance human understanding of mathematics?" One could also consider, "How do physicists advance human understanding of Physics (or Nature, or the Universe)?"
Jaffe and Quinn start their article, after the abstract, with "Modern mathematics is nearly characterized by the use of rigorous proofs. This practice, the result of literally thousands of years of refinement, has brought to mathematics a clarity and reliability unmatched by any other science. But it also makes mathematics slow and difficult; it is arguably the most disciplined of human intellectual activities."
So, now I am wondering if there are comparable articles since. Are there additional articles reflecting on Thurston's article, or the general question of what we are trying to accomplish as mathematicians and physicists (or chemists, biologists, . . . . ) besides earning a salary or paycheck?
https://www.physicsforums.com/threads/foundational-mathematics.1008334/
One of the recommended articles that popped up is William P. Thurston, "On Proof and Progress in Mathematics", Bulletin of the American Mathematical Society, Volume 30, Number 2, April 1994, pp. 161-177, which was written in response to an article by Arthur Jaffe and Frank Quinn, "Theoretical mathematics'': Toward a cultural synthesis of mathematics and theoretical physics," Bulletin of the American Mathematical Society, Volume 29, Number 1, July 1993, Pages 1-13. Reading Thurston's article prompted me to read the article by Jaffe and Quinn. It will take some time.
Thurston - https://arxiv.org/pdf/math/9404236.pdf
Jaffe and Quinn - https://arxiv.org/pdf/math/9307227.pdf
Of Jaffe and Quinn, Thurston writes the "article raises interesting issues that mathematicians should pay more attention to, but it also perpetuates some widely held beliefs and attitudes that need to be questioned and examined.
The article had one paragraph portraying some of my work in a way that diverges from my experience, and it also diverges from the observations of people in the field whom I’ve discussed it with as a reality check.
After some reflection, it seemed to me that what Jaffe and Quinn wrote was an example of the phenomenon that people see what they are tuned to see. Their portrayal of my work resulted from projecting the sociology of mathematics onto a one-dimensional scale (speculation versus rigor) that ignores many basic phenomena."
Thurston asks more or less, "What does one do as a mathematician?" He actually poses, "How do mathematicians advance human understanding of mathematics?" One could also consider, "How do physicists advance human understanding of Physics (or Nature, or the Universe)?"
Jaffe and Quinn start their article, after the abstract, with "Modern mathematics is nearly characterized by the use of rigorous proofs. This practice, the result of literally thousands of years of refinement, has brought to mathematics a clarity and reliability unmatched by any other science. But it also makes mathematics slow and difficult; it is arguably the most disciplined of human intellectual activities."
So, now I am wondering if there are comparable articles since. Are there additional articles reflecting on Thurston's article, or the general question of what we are trying to accomplish as mathematicians and physicists (or chemists, biologists, . . . . ) besides earning a salary or paycheck?