What are the odds that calculus is a colossal waste of time?

I have no idea what any of this means.

"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."  Albert Einstein

"Calculus is a blunt chisel used by engineers, despised by students and forgotten by almost everyone." Unknown

I loved studying math in high school and college, because I was pretty good at it. But now looking back on all the years of advanced math- algebra, trigonometry, and calculus- was any of that worth it? Am I using any of what I learned today? What would have been better to study to prepare me for life?

Math is a preferred pathway for nerds who aren't good at sports, as I was, and I even joined a team that went to compete with other teams at a local college. I can sort of see why some algebra is helpful- it trains you to work with variables and solve puzzles logically. Trigonometry is all about shapes, but I fail to see the relevance today unless you're an architect or engineer. And forget about imaginary numbers, operations in base 10 and beyond, square roots, or linear algebra. That leaves calculus- great for scientists and engineers, but worthless to the rest of us. Most secondary schools require 3 to four years of this advanced math to graduate, but does it matter? Colleges are a little more flexible, but by then the math nerds are hooked.

Not being an engineer, I've long ago forgotten most of the advanced math that I was so proud of. I even took multi variable calculus, which is about as far as you can go. My current career, accounting, is nothing but math, but on a much simpler yet more nuanced level. In math, the beauty is in finding the "correct" answer, of which there can be only one. Even the most complex formula can only have one answer, and finding it can be intensely rewarding. The real world, however, isn't like that at all.

In accounting, as in much of life, there is always more than one "correct" answer. It all depends on how one interprets data and the rules that apply to it. How can you count something that is always changing? Is there a formula to correct for the unexpected? How can you apply complex tax laws to large systems? Good luck.

1+1=2. The simplicity of that equation and the many that follow it make our universe seem predictable and orderly. Even tricky numbers like Pi and Infinity make sense when you know where they came from. Our world is complicated and messy, and no mathematical genius has been able to come up with an equation to explain all the variation and change that we see every day.

Rather than study calculus or algebra, I wish I'd been given more tools to study the field of probability and statistics. This is the real-world stuff. We have statistics for everything- baseball, elections, crimes, climate, stock prices, health outcomes, and much more. We just don't have the ability to make much sense of all that data. Statistics is mainly the scorekeeping of every known outcome, but it's an error-prone activity due to the enormity of what we try to keep tabs of. The real power comes from probability, which transforms statistics into useful predictions about what could happen in the future.

People aren't always comfortable with probabilities. If there's a 25% chance of rain, should you take an umbrella? If there's a 5% chance an operation could kill you, should you do it anyway? Life rarely gives us 0% or 100% chances- everything is always in the middle. Therein lies the risk, and no one likes too much risk. So a lot of us ignore the odds and do what we feel in our guts anyway. But if risks were accurately predicted, wouldn't the outcomes improve eventually?

Probability as an area of math is less popular because the answers are always couched in shades of gray. Our lizard brains want absolute certainty- impossible in the real world. We want right answers and standardized tests so that we can rank ourselves. So we make our students take years and years of math classes to learn formulas that they likely will never use in adulthood, especially now that computers and AI are available. (To be fair, though, every student should learn how to use a spreadsheet program- those are wonderful tools for simple and complex number crunching.) Much of math education is taught just to look good on school transcripts or to pass state math assessments for a school district.

Probability is not a static concept. What was likely 100 years ago may be impossible today. Probabilities must always be updated with new data to update the chances, also known as Bayesian statistics. Our cognitive biases and shortcuts don't like this constant updating, which makes aversion to probability and statistics even stronger. Why have the same economic theories persisted for fifty years even after being proven wrong? Why has climate change been ignored by huge swaths of humanity even as the statistical evidence keeps piling up? And why do so many people waste money on Powerball when the odds of winning are one in 300 million? "Never tell me the odds", is a powerful cry from Han Solo in Star Wars, but it gives license to reckless behavior when there are other things that might have better odds of success.

Probabilities are based on models of the world, and are thus full of unknowns, but they're better than flying blind. Especially as the odds get higher, it's worth paying attention to and even preparing for. For instance, as I write this in Mid-2025,

1- The probability of a recession in the US in the next year is judged to be 30-40%

2- The odds of another pandemic like Covid is about 2% per year, or 50% in the next 25 years.

3- Probability that the globe will pass the 1.5 degree warming target that was the upper goal of the Paris Agreement in 2015- 70%

4- The odds of an asteroid wiping out all life on earth in any year are about one in 100 million.

5- Probability of dying in a plane crash- 1 in 11 million. Car crash- 1 in 5,000

6- Likelihood that intelligent life exists on other planets- 45%

7- Odds of being diagnosed with cancer in a lifetime- 40%

8- LGBTQ+ individuals are estimated at 9.3% of the population, but that rises to 20% of generation Z members, with bisexuality being the most common.

9- The odds of living to age 100 are about 2%, with women much more likely to make it than men.

10- Odds of being struck by lightning- one in 1.4 million in any one year, or one if 15,000 over a lifetime.

Math scores are going down nationwide, partially because of the Covid epidemic, but I think there are other reasons. Schools are losing good teachers as political and religious priorities seem to be scaring them away. Cell phones are a tremendous distraction and brain drain that is hurting all studies. Computers and AI are doing a lot of the work for students, so they feel less of a need to learn and memorize basic or complex math.

Math is essential in personal finance, as well as in logically going through problems and finding solutions. There may not be one right answer anymore, but there are better answers than we've seen so far.

Probability is one field that could motivate a new passion for mathematics. I encourage everyone to look into it no matter what their age. I recently read a book- The Art of Uncertainty: How to Navigate Chance, Ignorance, Risk and Luck by David Spiegelhalter. Rather than review that book, I instead decided to put in my two cents about where math can help us and where it can waste time. We need to look more closely at what we are measuring and why, and make more informed decisions.

That doesn't mean turning everything over to an algorithm from artificial intelligence, because ultimately there are qualitative judgements that no machine can ever make. We need to dive into the grey areas of risk and uncertainty ourselves and chart a path towards a more humane, better functioning world guided by statistics and heart.