These are the #stories of #math that we celebrate, amplify and make central to the idea of #maths as a #objective #neutral #culture-free subject. #Math can do no #harm, and the #logical “pure math” thinking of #Mathematicians is worthy of emulation. But... 1/x
2/x ... "What about pure mathematics and mathematicians who merely prove theorems? Is there any #ethical component comparable to what you find in other fields of #science?" - R. Hersh in Experiencing #Mathematics
3/x One point of view: "there's no need for #mathematicians to have a code of #ethics, because what we do matters so little that we can do whatever we like."
(also from Experiencing Mathematics)
4/x "When #mathematical work may affect the public health, safety or general welfare, it is the responsibility of mathematicians to disclose the #implications of their work to their employers and to the #public, if necessary." @amermathsoc ams.org/about-us/gover…
5/x "There is an interesting paradox in how #mathematics is perceived by the #public at large. On the one hand, it is thought of as a world apart from practical #human existence, and often it is taught as pure abstraction, which reinforces this perception." - Reuben Hersh
6/x "On the other hand, it is supposed to be the most useful qualification for students preparing for high-prestige professions such as engineering and architecture."
7/x "#In discussing this #myth, we consider the role of #mathematics in broader #social #contexts including #elitist versus #democratic perspectives on who should become a #mathematician."
(correction, Reuben Hersh + Vera John-Steiner, in Loving and Hating #Mathematics)
8/x "Whenever #mathematics is employed to recommend or to set in motion a certain course of action, it is done on the basis of a criterion. One never knows the validity of the criterion nor does one know the full implication of putting a particular criterion to work." (Hersh)
9/x There is a dream: "a #universal message whereby all #human #problems whether #science #law or #politics could be worked out #rationally, systematically by #logical #computation. Cartesianism calls for world mathematization." - Hersh and Davis in "Decartes Dream"
10/x "It would be straining patience to try to compile a complete dictionary of #myths in #mathematics. We list a few; enough to illustrate our point, and to enable the reader (as an exercise) to extend the list at pleasure." (Hersh)
11/x "(1) Unity: There is only one mathematics, indivisible, now and forever. #Mathematics is a single/inseparable whole."
12/x "(2) #Objectivity: #Mathematical #truth or #knowledge is the same for everyone. It does not depend on who in particular discovers it; in fact, it is true whether or not anybody ever discovers it."
13/x "(3) #Universality: Mathematics as we know it is the only mathematics that there can be. If the little green men (and women?) from Quasar X9 sent us their math textbooks, we would find again A = πr2." (Hersh)
14/x "(4) Certainty: #mathematics possesses a method, called “#proof” or sometimes “rigorous proof”, by which one attains absolute certainty of the conclusions, given the truth of the premises."
15/x "Myths, of course, need not be true; they need to be useful. Whatever the reason, it is clear that #mathematicians want to believe in unity, objectivity, universality, and certainty, somewhat as Americans want to believe in the Constitution and free enterprise"
16/x "“But,” says the Platonist, “how can you explain the fact that always and everywhere, regardless of time and place, politics or religion, race or sex, 2 + 2 always equals 4?" (Hersh)
17/x "The only way to account for it is to say it’s an #objective truth, which we all recognize because it’s an objective truth. Otherwise, the universal agreement that 2 + 2 = 4 would be an inexplicable miracle.”
18/x "To this I answer, “It’s bad logic to say something must be true because you can’t think of any other explanation. That’s how philosophers used to prove the existence of a Supreme Creator—they couldn’t conceive any other way for there to be a universe." (Hersh)
19/x tying back now to the beginning of the thread: "#Nuclear #weapons #mathematics is an accepted component of American mathematical life. It usually isn’t even considered controversial."
20/x "That is why it can slip on unintentionally and uninvited into an undergraduate competition. It’s not hard to guess what message this problem conveyed to the contestants." (Davis and Hersh, Descartes' Dream)
21/x "It will be objected, what is wrong with teaching nuclear weapons mathematics? If the #military wants such mathematics, isn’t at the job of #mathematicians to supply it and to train those students to perform it who choose to do so?"
22/x "This attitude treats the military is simply one more customer, no better or worse than any other."
23/x “The social and physical worlds are being #mathematized at an increasing rate. We’d better watch it because too much of it may not be good for us” #math #maths (in Descartes' Dream)
24/x the "widespread sentiment that the way to arrive at #objectivity in the real world is to travel the mathematical road. If a subject can be mathematized, this automatically guarantees objectivity."
26/x "#science, and its abstract #mathematical formulations, has imposed its own #reality on human #values and behavior."
27/x when "#Mathematics affects individual #people, we must watch out and be careful, for the #math is often taken for granted; is rarely questioned. The very existence of the characteristic features of math attracts the world and invites the world to apply them, come what may."
28/x one aim of " ...the application of #mathematics to #people is to be able to compare two individuals or groups of individuals to be able to arrive at a precise and definitive opinion as to which is taller smarter richer healthier happier, more prolific..."
29/x "which (person(s)) is entitled to more goods and more #prestige and ultimately, when this #weapon of thought is pushed to its #logical limits and cruelly turned around, which is the most useless and hence the most disposable." #SocialJustice #math (Descartes' Dream)
24/x the "widespread sentiment that the way to arrive at #objectivity in the real world is to travel the mathematical road. If a subject can be mathematized, this automatically guarantees #objectivity."
26/x "#science, and its abstract #mathematical formulations, has imposed its own #reality on human #values and behavior."
