WiltedSpinach
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Comment · 8 years ago
Comment · 9 years ago
Dr. Zeilberger writes a rather pleasant rant. He appears frustrated with the lack of imagination in mathematicians which occurs when they focus too strongly on the axiomatic nature of mathematics, and seems to wish that we take a step back from the powerful axiomatic tools we have developed, so that we may search for what is 'really true about the world' rather than 'playing a mathematical game/believing in a mathematical religion'.
Three specific complaints he has involve a belief in infinity (and limits), which he asserts do not exist in the real world; a delay in the publication of a pair of papers on which he worked, due to a variety of circumstances; and a "pernicious" influence of axiomatic mathematics which leads to "stupid" questions such as Hilbert's Second Problem.
The failed publication of one paper is particularly notable, as it claimed a counterexample of Fermat's Last Theorem (according to Dr. Zeilberger's "Opinion 123", on his Rutgers website), and (ibid) was recognized by Andrew Wiles himself as one of three possible counterexamples: the reason given for this oversight was in fact the acceptance of the decidedly non-rigourous statement "it is easily seen ..." (ibid). This particular instance seems to contradict the main thrust of Dr. Zeilberger's rant against a mathematics overburdened by rules.
Unfortunately, little example of what mathematics SHOULD look like is offered - beyond a statement that 'obvious things should be treated as such' and an assertion that infinities and continuities do not occur in real life/nature/the universe. While such a statement may be understandable coming from a respected (and clearly accomplished) combinatorist such as Dr. Zeilberger, physics has yet to demonstrate conclusively that space and time are discrete - undisproven interpretations of quantum mechanics exist which allow for continuities, and 'the size of the universe' is defined as that which we can see (ie, within ~13.8 billion light-years of Earth/Sol) so that actual infinities are ruled out only because of our inability to perceive them.
Perhaps Dr. Zeilberger needs to think outside his own discrete box.
One could just as easily state that a 'rational' society should celebrate: a stable number of jobs (if one is anti-technologically inclined, or if one happens to believe that society is harmed by rapid change); or a growing number of jobs (the rapid change view + population growth, or a belief that more jobs mean people have found more problems to be solved).
But one could also move away from the direct 'jobs' concern and argue that a 'rational' society would be better at finding ways to address the need humans have for being valuable to their society (often expressed here in the US in terms of having a job) and ensuring that people have enough capital to live on a year-to-year basis, whether by changing the expression of those needs and giving a universal basic income or by finding better jobs or perhaps even by going with a strongly progressive income tax and actually supporting small businesses.
Many of the examples I have provided have been argued in the past at some point or another (and my short list is by NO means complete), and one could certainly talk about whether empirical evidence seems to support or contradict each of these points (though note that there are likely multiple interpretations of the data!), but ultimately our society is made of people and articles such as this suggest that we have built a society that systematically fails to support the values of its members. So maybe we should start talking about those values and quit going on rants about 'oh, everyone else is irrational'.
Relevant XKCD: https://xkcd.com/610/