Why the importance of math is inversely proportional to your aptitude for natural reasoning.

In a recent discussion, I contended that the importance of math is inversely proportional to a person’s aptitude for natural reasoning (i.e. the poorer your reasoning skills, the more math you should learn). Needless to say, there were more than a handful of dissenting voices (most eluding to various levels of delusional snobbery), but nevertheless, I stand by my position wholeheartedly.

Having mooched around the technology arena for more decades than I care to mention, I’ve had the opportunity to rub shoulders with just about every kind of person you can imagine. Whilst each generally exhibited their own personality and unique nuances, all appeared to fit comfortably within one of the following four categories:

1. Exceptional natural reasoning skills, with additional contemporary mathematical knowledge.

2. Exceptional natural reasoning skills, with no contemporary mathematical knowledge.

3. Nominal natural reasoning skills, with additional contemporary mathematical knowledge.

4. Nominal natural reasoning skills, with no contemporary mathematical knowledge.

Obviously, it would be nice if everyone could claim their place within category #1, but the vast majority of us simply aren’t built that way: most of us begin our journey at category #4, accompanied by a vague hope that diligence, perseverance, and hard work will eventually edge us towards category #3. Nonetheless, our personal indignations notwithstanding, category #3 is not to be sniffed at, for it allows us to compete against category #2 using the ratified methods of those clever enough to reside within category #1.

To illustrate my point, consider the following problem:

In March, I purchased a pair of shoes discounted by 25% from the previous month. If I paid £175 in March, what was the RRP in February?

Surprisingly, whilst the majority category-#4 adults are likely to fall at the first hurdle, most 6th graders will derive the answer in under a minute. So what’s the deal here? Are today’s 6th graders infinitely more intelligent than those of yesteryear? Well, probably not, but their mandated curriculum certainly positions them closer to category #3 than those who abandoned their scholastic careers more than twenty years ago.

So why exactly do these adults fail? Well, it’s simply a matter of perception: as the original RRP is not known, there is no perceived value upon which to apply the original 25% discount. To all intents and purposes, it appears insoluble. Of course, the perceived discount does, in fact, scale reciprocally with the discounted RRP (i.e. if the discounted RRP is 75% of the original, then the perceived discount also changes by the reciprocally proportional value 1/75%), but this is not naturally intuitive to the majority of people who are unaccustomed to thinking in algebraic terms.

For our 6th graders, however, they need neither intuition nor natural reasoning to effect the appropriate answer: they need only apply a simple set of ratified and well-rehearsed theorems handed down by their betters:

Specify the problem:

£175 = RRP - 25% * RRP
     = RRP - 0.25 * RRP

Combine like terms:

£175 = 1 * RRP - 0.25 * RRP
     = 0.75 * RRP

Solve for RRP:

£175 / 0.75 = RRP = £~233.33

In short, mathematics is a proven language for describing phenomena that would otherwise remain elusive to all but the best of us. Furthermore, the poorer your reasoning skills, the more time you should dedicate to learning its nuances and dialects. At the end of the day, the person who’ll steal your promotion will likely be better prepared rather than better endowed.