characters What Is Mathematics Really?
review What Is Mathematics Really? 107 Nd Russell David Hilbert and Rudolph Carnap followed by the mavericks who saw mathematics as a human artifact including Aristotle Locke Hume Mill and LakatosWhat is Mathematics Really reflects an insider's view of mathematical life and will be hotly debated by anyone with an interest in mathematics or the philosophy of scienc Hersh sets out to define the parameters of a philosophy of maths his best answer being a socio historiic cultural context resolving the Platonist formalist split the ethereal real zone of Platonism being replaced by the collective human mindbrain The delight of the book though is the later sections on the history of philosophy of maths where he namechecks many s a classic and the section on basic principles of maths I say basic but the piece on Godel s incompleteness theorem
review ´ eBook, PDF or Kindle ePUB Õ Reuben Hersh
review What Is Mathematics Really? 107 Most philosophers of mathematics treat it as isolated timeless ahistorical inhuman Reuben Hersh argues the contrary that mathematics must be understood as a human activity a social phenomenon part of human culture historically evolved and intelligible only in a social context Hersh pulls the screen back to reveal mathematics Peace in Troubled TimesFor many including myself mathematics is comforting In an era of fake news worldwide illness and economic uncertainty mathematics provides proof of another reality which is harmonious universal and eternal Or so it would seemIn fact mathematics like all literature is none of these things Mathematics is of course a human artefact It is a language which consists of a vocabulary a grammar and a community which employs these enthusiastically Arguably mathematics is the most refined language ever producedOr rather set of languages There are apparently some 3400 recognised branches of mathematics Many of these have their peculiar dialects which are unintelligible to members of other mathematical communities At least some have never been translatedHersh identifies two historical schools of thought which have dominated popular as well as professional discussion of mathematics Platonists and Formalists Platonists consider mathematics as a kind of religion Numbers they believe exist independently of human thought about them They constitute the basic fabric of the universe and determine its orderliness and predictability For them mathematics is realityFormalists dismiss this uasi spiritual view Their opinion is that mathematics is a game the rules of which are entirely arbitrary If Platonists are the religious enthusiasts of mathematics Formalists are the agnostic clergy who have lost the certainty of belief but continue to exercise their ritualistic duties regardlessHersh dislikes both Platonists and Formalists His credible claim is that mathematics developed and continues to develop because it is useful And it s usefulness varies so that what mathematics means and how it develops also varies continuously There is no fixed mathematical method by which good mathematics can be distinguished from bad There are just mathematicians talking among themselvesThis fact that mathematics emerges from its adherents discussing mathematics may appear a truism What else could be happening But the recognition that mathematics emerges from a restricted community is an important insight The usefulness of mathematics is not that of engineers or architects or astrophysicists or people filing tax returns These and other users of mathematics eventually benefit from the products of mathematical discussions in their own work but they are not mathematicians We may tolerate mathematicians among us because of what their work allows the rest of us to do but mathematicians could care less It s not why they do mathematicsThe practical or in their minds pedestrian usefulness of the work of mathematicians does not concern them Even a brief exposure to number theory for example is sufficient to convince most outside the mathematical community or even outside the community of number theorists that the things mathematicians are concerned about are essentially trivial The strange and often captivating relationships among numbers are simply alien to practical experience The non mathematician can only ask Why bother And the answer to this uestion must be the same as it is to the issue of literature in general There is no reason for mathematics other than itself Mathematics is a form of highly refined esoteric poetry Its form and subject matter is not to everyone s taste But neither is the Iliad or The Wasteland or Finnegans Wake It takes considerable linguistic skill and aesthetic fortitude to comprehend the content of mathematical poetry Success in such an endeavour is as usual its own reward
Reuben Hersh Õ 7 review
review What Is Mathematics Really? 107 As seen by professionals debunking many mathematical myths and demonstrating how the humanist idea of the nature of mathematics closely resembles how mathematicians actually work At the heart of his book is a fascinating historical account of the mainstream of philosophy ranging from Pythagoras Descartes and Spinoza to Bertra The book being reviewed here What is Mathematics Really is engagingly written I found the literary style to be highly palatable However I do not concur with the author s philosophy of mathematics Admittedly he was a professional mathematician while I m a mere amateur mathematician and amateur philosopher Nevertheless the stance I take on the philosophy of mathematics is not idiosyncratic I am essentially Platonist in my worldview with respect to the ultimate nature of mathematics Platonism in mathematics is the most widely held view of modern mathematicians or so I believe This puts me in favorable company among professional mathematicians Rueben Hersh s philosophy of mathematics is humanist social historical He stated that his favorite philosopher in college was David Hume There s little wonder that Hersh is a left leaning humanist with an apparently atheistic worldview On pages 248 249 Hersh states the following Mathematics is another particular special social historical phenomenon Its most salient special feature is the uniuely high consensus it attains My reply to this assertion is this Is that consensus not because mathematics asymptotically approaches the objectively existing perfect and infallible mathematics Note that the study of physics leads physicists deeper and deeper into a better precise and valid philosophy of physics Newton s theories of space and time were corrected by Einstein s deeper insights into the true nature of space and time In like manner mathematicians learn and about the true nature of mathematical realities even as physicists learn about the true nature of mass energy and space time Overall I give Hersh s book moderately high marks notwithstanding his unpalatable atheist humanist social philosophy that s espoused in his engaging book
- What Is Mathematics Really?
- Reuben Hersh
- 22 October 2019 Reuben Hersh