“Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” – Bertrand Russell
For the better part of the past 60 years, mathematics has been my source of solace and refuge – the place where I turned for order, serenity, and beauty when any, or all, of those were lacking in the world around me. As I approach my 62nd birthday later this month, however, that sanctuary has been breached.
It would be reasonable for you to assume that I am referring to the assault on sensibilities that has been reality of the mathematics of the pandemic. Or perhaps you think I am referring to the assault on logic that has characterized the attempt to report the mathematics of the pandemic. But you would be wrong. No, this is something much more personal – the morbid mathematics associated with deciding whether to begin receiving social security benefits on my 62nd birthday.
“Math is the only place where truth and beauty mean the same thing.” – Danica McKellar
The Social Security Administration informed me that I am eligible to start receiving a monthly payment when I turn 62 later this month. However, if I wait another five years (actually 4 years, 10 months) until I reach full retirement age to begin receiving payments, my monthly payment will be $1,000 per month higher. When will it be more advantageous to me to have begun receiving payments at 67 rather than 62? The mathematics to answer that question is straightforward, as it usually is.
For the sake of simplicity, let’s say that my monthly payment would be $2,000 if I begin this year and $3,000 if I wait five years.
I can attack the question graphically.
I can use Algebra to set up a system of equations to compare the cumulative payments over time (where x is the number of months starting at age 62).
I can back into an answer by determining how much I will receive in payments during the five years between age 62 and 67.
No matter how I slice it, the mathematics is telling me that up until April 2036 I will take in more money by beginning social security payments this year at age 62. Beyond April 2036, when I will be 77 years old, beginning payments at age 67 will produce more money.
“The mathematical sciences particularly exhibit order, symmetry, and limitations; and these are the greatest forms of the beautiful.” – Aristotle
The problem, of course, is that the calculations above provided critical information to help me answer the important question of when to start payments, but mathematics didn’t provide the answer to my real question – Should I start collecting social security payments now? To answer the question, I have to determine when I am most likely to die, or how long I am likely to live, if you prefer. (I mentioned morbid, right?)
I can call on various disciplines of applied mathematics to help me determine my probability of living to age 77, based on any number of factors I decide to include in a model – some generic (e.g., sex, race, current age, location), others quite specific to me (e.g., general health, physical fitness, family history).
I can also consider my motivation to live until 2036 and 77 years old, because I believe that makes a difference.
- Harvard will celebrate its 400th anniversary in 2036, and a group of friends agreed at the Harvard 350 celebration that we will meet again at Harvard 400. I wouldn’t want to let them down.
- I would like to see how we work our way through this climate change thing.
- My daughter will be in her 40s. I needed lots of good advice from my father in my 40s.
Other factors not mentioned above would also have to be considered when making my decision, things like:
- limitations on earnings if you start collecting social security payments at age 62,
- the impact on the social security payments my wife will receive after I die, and
- our likely expenses between now and 2026, or before and after 2036 (e.g., how many albums with related merch is Taylor Swift likely to release in the next 5 years v. 15 years v. 25 years).
Mathematics can help me build up and tear down arguments in favor of one position of the other. It helps me organize my thoughts, but mathematics cannot make the decision. Only I can do that. And for me, that is the true beauty of mathematics.
“I’m sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.” – Malcolm X
The sad fact, however, is that many Americans give up on mathematics long before they get to the good part – the uncertainty – using mathematics to engage in arguments (even if they are with yourself).
When it comes to Reading instruction, people talk about learning to read shifting to reading to learn. Without falling into the academic rabbit hole about the accuracy of the statement, the implication is that at some point in K-12 instruction, the skill that is Reading is applied for other purposes.
I know of no similar statement or sentiment about mathematics instruction. Through high school, we continue to pile on new and more complex skills, but never truly get to their use. Sure, there are some word problems here and there. But will I ever need to know at what time the two trains will arrive at the same place? Or how long it will take to fill/empty the tank with water coming in one large pipe and going out through three smaller pipes? (hint: see above)
We rarely ever get to the fun part of using mathematics in K-12 education, the part where we put the ability to make accurate calculations to productive use. In fact, in the past several years we have gone out of our way to develop high school science courses that require little, if any, mathematics. The Common Core State Standards in English Language Arts were named English Language Arts & Literacy in History/Social Studies, Science, and Technical Subjects – explicitly connecting ELA knowledge and skills to their use across content areas. The writers of the Mathematics standards, in contrast, couldn’t find a good way to connect mathematics practices (i.e., the use of mathematics) with the standards for mathematical content.
We have created a culture that is happy to treat math as a four-letter word (even the five-letter version in the United Kingdom). We are quick to either weaponize or vilify algorithms as if they were an AR-15. Algorithms don’t create bad radio programming, restrict our searches on Google, or create social inequities, people do – at least until we cede total control to the machines.
I have had enough. I think I’ll go for a walk and listen to some music. It will probably help me calm down, and according to the math, might even improve my chances of making it to 2036.