Applied mathematics: lessons in the moral sciences

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The Ethic of Mathematics

While some mathematicians argue that mathematics is (or should be) apolitical, others subscribe to what I call an “ethic of mathematics,” a conviction that the practice of mathematics embodies profound moral lessons on how to live well with others. They feel an ethical imperative to apply values embedded in mathematical practice globally as a means of promoting peace and cooperation.3 One such value is internationalism. In 1882, just after the Franco-Prussian War, the Swedish mathematician Gosta Mittag-Leffler (1846-1927) founded Acta Mathematica, an explicitly international journal of mathematics. By actively soliciting and publishing the work of the most brilliant mathematicians from both Germany and France, he set out to affect some reconciliation between the two countries. During and after World War I, he once again eagerly assumed the role of mediator, this time working through the pages of his journal to reunite both the English and the French with the Germans (Dauben 1980). Ever anxious to put politics aside, the Englishman Hardy shared Mittag-Leffler’s desire to re-establish friendly relations with German mathematicians and scientists as soon as possible after the First world War. But their efforts to return to normalcy after the cataclysm met with stiff resistance.
Hardy found that rather than adhering to the spirit of internationalism and promptly renewing collaborations that had been sundered by the war, his colleagues joined with the vast majority of their compatriots in harboring much hatred and resentment against the Germans. A good example of the “imbecilities”4 he encountered appears in a letter from an English scientist published in Nature, the pre-eminent English science journal: “[I]t is impossible to dissociate the mental attitude of the population of that country, by no means excepting the highly educated and scientific classes, from the world-conquering aspirations of their rulers, or from the barbarous atrocities committed by them in pursuit of that national ideal.” (Walsingham, 1918) It appears that for some, the value of internationalism is not as deeply embedded in their mathematical practice as one might have hoped.
The debate about the appropriate relationship between mathematicians/scientists5 and politics, in particular their participation during periods of war and international conflicts, erupted with great passion once again in reaction to the recent U.S. military action in Iraq. On being asked to review a manuscript for a pre-eminent American physics journal, Physical Review, Israeli physicist Daniel Amit e-mailed the following reply: “I will not at this point correspond with any american [sic] institution. Some of us have lived through 1939” (Amit 2003).6 Martin Blume, editor of the journal, while respecting the author’s decision not to review any further papers, also takes the opportunity to ask him to “consider the following in hopes that in the not too distant future you will decide to review for us again. We regard science as an international enterprise and we do our best to put aside political disagreements in the interest of furthering the pursuit of scientific matters.” Amit replies that although he would like to be able “to share the honorable sentiments” expressed by Blume, he adamantly maintains that “Science cannot stay neutral.” In a haunting echo of the 1918 letter in Nature, he proclaims “What we are watching today, I believe, is a culmination of 10-15 years of mounting barbarism of the American culture the world over, crowned by the achievements of science and technology as a major weapon of mass destruction.” Thus, he says he can no longer see himself “sharing a common human community with American science.”
There is a further ironic twist to this storyline, which is not lost on Amit.7 In an attempt to support the Palestinian struggle against Israeli occupation, academics in many countries have been advocating a boycott of Israeli scholarship. In response, the International Mathematics Union issued a statement in which they explicitly “oppose holding individual mathematicians liable for the actions of their governments.”8 This recurring debate focuses our attention on several key questions. What does it mean to practice a “moral science”? Should scientists be held responsible for or even be concerned with the actions of their governments, or does “good” science transcend politics?
The search for answers to these questions uncovers another moral precept embodied in mathematical practice, its democratic “anti-authoritarianism.” Every new mathematical result—whether submitted by a proven mathematician or a novice— must be verified by referees, each step painstakingly checked by other members of the community, before it is accepted as a theorem. All claims and views, even those of the “experts,” are always open to question. Theoretical physicist Lawrence Krauss invokes this principle to argue that it becomes the ethical responsibility of “citizen-scientists” in a democracy to question the actions and claims of government experts when the warnings of major scientific organizations go unheeded. For example, he publicly questions his government’s commitment of billions of dollars to the deployment of a missile defense system (thereby also abrogating a longstanding international treaty) while ignoring a recommendation by the American Physical Society that such deployment be delayed until the success rate of the system, presently estimated to be at best 40 percent, is demonstrated to be workable against realistic threats (Krauss 2003, 3).9 His application of the anti-authoritarian value embedded in mathematical and scientific practice leads him to conclude that there are instances when it is unethical for scientists to refrain from engaging in politics.

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