Prominent mathematician William Thurston was praised by other mathematicians for his intellectual generosity. But what does it mean to say Thurston was intellectually generous? And is being intellectually generous beneficial? To answer these questions I turn to virtue epistemology and, in particular, Roberts and Wood’s analysis of intellectual generosity (Intellectual virtues: an essay in regulative epistemology. Oxford University Press, Oxford, 2007). By appealing to Thurston’s own writings and interviewing mathematicians who knew and worked with him, I argue that Roberts and Wood’s analysis nicely captures the sense in which he was intellectually generous. I then argue that intellectual generosity is beneficial because it counteracts negative effects of the reward structure of mathematics that can stymie mathematical progress.
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We will see that intellectual generosity involves a concern with intrinsic over extrinsic intellectual goods. However I am agnostic on the question whether intrinsic or extrinsic goods are ultimately superior.
Although Franklin didn’t know this, her own data had been crucial to Watson and Crick’s work, but they had used it without her knowledge and without giving her credit (Roberts and Wood 2007, p. 298).
There were, however, some doubts about the reasons Thurston was slow at publishing his theorems and proofs. More on this below.
Nonetheless, some noted that Thurston was not perfect. For example, he would sometimes miss the deadlines for submitting letters or reports that were needed for job applications or promotions and did not take an active approach to advising students.
I am grateful to two anonymous reviewers for raising the issues considered below.
Thurston did, however, publish parts of it (Thurston 1994, p. 176).
Roberts and Wood did note that a concern with intrinsic over extrinsic intellectual goods characteristic of intellectual generosity can help researchers persevere where others might give up and so potentially generate new intrinsic intellectual goods in this manner (Roberts and Wood 2007, pp. 301–302). They also pointed to specific ways in which McClintock’s intellectual generosity to Creighton generated intrinsic intellectual goods (Roberts and Wood 2007, p. 302).
I am grateful to an anonymous reviewer for pointing out relevant connections between intellectual generosity and social epistemology.
The arguments that I make in this section are a modified and shortened form of arguments I make in Morris (n.d.).
See https://mathscinet.ams.org/mathscinet/msc/msc2010.html for the full list.
Such scenarios happen in practice: “Fields in the mathematical sciences are mature enough so that researchers know the capabilities and limitations of the tools provided by their field, and they are seeking tools from other areas” (National Research Council 2013, p. 97).
Thanks to Bonnie Gold for alerting me to Erdős’s generosity.
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I am very grateful to Ian Agol, Yakov Eliashberg, Yacin Hamami, Bonnie Gold, Joel Hass, Erich Kummerfeld, Curtis McMullen, Yair Minsky and Alan Weinstein. I am also very grateful to participants at both the Mathematics in Practice conference held at Stanford University in May 2019 and the MidWest Philosophy of Mathematics Workshop held at Notre Dame in November 2019. Finally I am very grateful to three anonymous reviewers for their many helpful comments and suggestions. This work was partly undertaken while I held a Postdoctoral Scholarship at the Suppes Center for History and Philosophy of Science at Stanford University.
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Morris, R.L. Intellectual generosity and the reward structure of mathematics. Synthese (2020). https://doi.org/10.1007/s11229-020-02660-w
- Virtue epistemology
- Intellectual virtues
- Intellectual generosity
- Mathematical practice