Congratulations to the blogger -- he has rediscovered the formulate first described in the 16th century by the French mathematician Vieta.
Formally, if one expands <math>(x-r_1) (x-r_2) \cdots (x-r_n),</math> the terms are precisely <math>(-1)^{n-k}r_1^{b_1}\cdots r_n^{b_n} x^k,</math> where <math>b_i</math> is either 0 or 1, accordingly as whether <math>r_i</math> is included in the product or not, and ''k'' is the number of <math>r_i</math> that are excluded, so the total number of factors in the product is ''n'' (counting <math>x^k</math> with multiplicity ''k'') – as there are ''n'' binary choices (include <math>r_i</math> or ''x''), there are <math>2^n</math> terms – geometrically, these can be understood as the vertices of a hypercube. Grouping these terms by degree yields the elementary symmetric polynomials in <math>r_i</math> – for ''x<sup>k</sup>,'' all distinct ''k''-fold products of <math>r_i.</math>Mathematical mental artifacts are special stories with incredible mutation-resistent properties, memes which compel their host with astonishing power and insistence to interpret and extract from them the same conclusions and patterns and behaviours that other hosts infected with the same meme did\do, or at least prevent one host from interpreting or concluding the opposite of what most other hosts interpreted\concluded.
That is, Mathematical Reasoning is a distributed mind-consensus 0-communication algorithm, a way for minds (instantiated in brains, silicon chips,spacetime foams,...) to agree on something while never actually explicitly arguing or debating or handshaking in any way. The set of all objects and states Mathematical Reasoning is capable of agreeing on is by definition Mathematics.
Discovering sentient aliens would shed much light on this.
It's possible to maintain mathematics is discovered and its objects are subjective. This would be akin to the kantian position, in which mathematics constitues something like the formal structure of subjective experience itself. ' Either way, the options arent "invented subjectivity, vs. discovered platonism
Joke aside, yeah various people pointed that out to me so I quickly added an edit at the end of the post. Thanks :)