Essay - Mathematics How Mathematics Grows: the Role of the Individual and...

Mathematics

***** Mathematics Grows: The Role of the Individual and ***** Culture

Influences the Course of Ma*****matical Discovery

There are many influences on the course ***** ma*****matical discovery. The dominant forces influencing mathematical ***** are individual and culture, as pointed out by the reading. There is as much subjectivity in mathematical computation as there ***** science, which is part of the reason so ***** ***** mathematics ***** ill understood and often mis*****terpreted. As the reading points out those not well versed in mathematics or those with little training often have an imperfect notion of how it operates and how solutions or mathematical proofs must be derived. Often what seems correct is later found in*****, ***** vice versa. This is evidenced by the example ***** the reading, whereby professor Hans Rademacher of the University of Pennsylvania, a leading ********** at the time, mistakenly believed he solved Riemann's Hypo*****sis (p. 60) only to be dis*****roved *****. The ***** and ***** directly influence mathematical discovery. There isn't really a dichotomy between the individual and culture; they simply ***** mathematics differently. For example, an ***** who is br*****i*****t and capable ***** great mathematical feats may at the same time think outside of the scope ***** wh***** the culture he or she lives within may consider "*****dinary." Thus this person's brilliance or folly will either be embraced or rejected depending on the fit with the ***** at the time the soluti***** or hypothesis is presented. The reading for example, points out the case of Hermann Grassman, ********** work is today considered genius, however during his time was consider obscure and mystical because the work ***** not in l*****e with the culture Grassman grew up in.

The creat*****g and practice of ***** are not the same. The ***** of mathematics is more aligned ***** cultural norms and ********** is ***** acceptable practice during the time ***** is accomplished. Creation however, may involve ***** extremes of an individual, or an individual's ability to tap in***** a genius that may seem unusual or ***** at the time it is conceived or at the time an idea is realized.

M*****hematics as the read*****g suggests posses many characteristics, being ***** from individual ***** but thriving ***** when the culture or wider community ***** described by the text accepts the principles and applications surrounding it (p. 64). Individual discovery alone *****, is not responsible for mathematics. The text also notes that economic and social ********** can stimulate mathematical discovery. Mathematical discovery however, is something ***** persists regardless of the historical time or culture dominating. The text notes that many theorists favor the "doctrine of culture" so one ***** acknowledge the influence ***** has on *****. The text suggests the dichotomy between ***** individual and the doctrine of the culture is false, an argument similar to that of mind over matter; one can conclude simply that *****s ***** matter temporarily ***** ***** dominates the field of mathematics ***** wider ***** periods. That culture is inextricably linked ***** mathematical inquiry ***** a fact