The Case for Sharpening Your Math Skills in the Age of AI

With the rise of AI, business leaders may be wondering: Is it time to outsource math to machines, freeing managers to do more managerial things? The answer: Absolutely not. Math is the core language of business. And it’s more important than ever for business leaders to speak it fluently. This is true across virtually all functions and levels, from CxOs to warehouse managers. Paraphrasing Charlie Munger: Making business decisions without knowing the numbers is like fighting with one leg tied behind your back. It’s not going to end well. It is true that AI has some impressive capabilities in math. Large language models (LLMs) have achieved elite status at math competitions, while we humans seem headed in the opposite direction. At first glance, that looks like a gross mismatch, “game-over” for us. But it’s not the full story. AI is particularly good at finding exact answers to exactly stated questions, an ability Sanjoy Mahajan calls “academic” math. Business math, however, is different. It requires practical, approximate, adaptable solutions to the fuzzy, fluid, squishy problems real-life actually hands out. Such problems expose AI’s weak points, and reveal the strength of human reasoning, creativity, and common-sense. You don’t need to be able to compose Shakespearean verse to speak good conversational English. Similarly, you don’t need to be able to precisely solve differential equations to speak useful business math. What you absolutely must be able to do is this: Structure and solve real-world problems in practical and flexible ways. This is the kind of math fluency managers need. Like any language, it’s a learnable, “use it or lose it” skill. And mastering it can even help unleash the full power of AI, guided by humans who know exactly what they want from it. I have a math degree from the University of Cambridge, home of legends like Isaac Newton, Srinivasa Ramanujan, and Alan Turing. I am a longtime member of Mensa, a group known for solving crafty logic puzzles. And I have two decades worth of apprenticeship-style learning in the numbers-driven fields of data analytics, strategy consulting, and investing. These experiences have helped me hone a set of business-focused math tools which are both timeless in their utility and timely for the AI era. They relate to sanity-checking computational models, thinking probabilistically, and being aware of multiplicative dynamics. I will outline these below as: TRY, DO, and WIN. TRY = Think and Reason for Yourself Inattentional blindness, a psychology concept, says we are sometimes so super focused on irrelevant details that we completely miss the big picture which matters. Maybe you’ve seen the famous “gorilla in the room” video. The above is a real danger when it comes to business math. For example: In the dot-com boom of the late 1990s, managers became hyper-obsessed with measuring “eyeballs” and lost sight of the gorilla in the room: that cash flow is necessary to create business value. Simple calculations showed that the cash flow math didn’t come close to adding up. Unsurprisingly, many dot-com companies went bust. Scott McNealy, then CEO of Sun Microsystems, used elementary reasoning to show that many widely-accepted core assumptions in that era were, in fact, ridiculous. His post-mortem assessment: “What were you thinking?” In the Great Financial Crisis of 2008–09, experienced analysts built detailed financial models which assessed U.S. banks like Lehman Brothers as “buy” rated stocks and “A” grade credit risks mere weeks before Lehman and others collapsed. While this was happening, some relative outsiders like Michael Burry looked at home-loan securitization by these banks, did basic math, and concluded: This makes no sense. They were correct. “How to miss by a mile” is a 2014 memo by venture capitalist Bill Gurley. It makes the case that experts appraising the value of Uber may have had the world’s best financial model, but its core assumptions were “off by a factor of 25 times.” History has validated Gurley’s reasoning. His point: Business analysts engrossed in building complex spreadsheets can miss fundamentally re-scaling key inputs like market size. Especially so for disruptive businesses that have no existing comparables. These are high profile examples, but the issue they highlight applies at every level: It’s easy to “blindly” trust detailed numbers coming out of a fancy model. That may be fine. But it’s no replacement for thinking and reasoning for oneself. The antidote to the above is to always do your own simple, common-sense, sanity-check math. To borrow from a famous saying: It is better to be approximately right (using your own mind) than precisely wrong (using flawed model outputs). Here are three skills one can learn and practice to proficiently do the above: Build numerical intuition: I use an unusual calculator which “thinks only if you think too.” When you enter a calculation, the calculator first asks for your rough, best-guess answer. If your guesstimate is in the approximately right ballpark, it will oblige with the exact solution. Otherwise: Think harder, try again. (Find it here.) Use a problem-solving framework: I was trained in the legendary McKinsey method. It works by iteratively building, testing, and refining simple hypotheses using relevant facts and approximate math. And it applies to virtually any problem. (It’s taught here.) Learn mental-math tricks: Mahajan teaches six practical strategies I use to simplify the hairiest of problems: Dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. (See here.) DO = Decisions vs. Outcomes Perhaps the most powerful math lesson I have learned in my career is this: We make decisions. The world observes outcomes. These two things are related. But they are not the same. While pursuing my MBA, I took a finance class in which we were assigned a simple Oil Baron game for homework. It’s a computer simulation with basic inputs: the cost of drilling for oil, the probability of hitting oil if you choose to drill, and the profit you make if you do hit oil. (If you drill and don’t hit oil, your loss equals the drilling cost). Everyone in the class played this game 100 or so times. The cost, probability, and profit above would change each time. But the decision remained: Drill or no drill? Each round was independent (prior outcomes didn’t change future inputs). But the software kept a running tally of wealth across rounds by adding or subtracting profits and losses. The next day, our finance professor made two points based on the results of the above: Decisions: Every instance of the above game had a precisely correct answer: One can figure out whether to drill or not drill by using probabilistic decision trees to calculate expected values. And yet, only 20% or so of the class had made the correct decision every time. The rest either didn’t know how to do the math or deliberately chose to roll the dice and gamble. (MBA students are busy, and gambling is faster than calculating.) Outcomes: The folks who made the mathematically correct decision every time—the best you can do with factors under your control—were clustered around the top 10%–15% of final cumulative wealth. They did excellently. But here’s the thing: At least 10% of the class had more wealth than them simply by gambling. Indeed, the top 1% ended up with 10x more wealth than the best-decision cohort. Decisions aren’t outcomes. Does this mean gambling is better than trying to make the mathematically best decision? No. Gambling may create a few outlier winners, but it mostly creates a lot of busts. As the professor concluded: Unlike classroom games, real-life information is never perfect. But using probabilistic logic, like decision-trees, with the best inputs possible remains the best way to make good decisions. Indeed, if you do this consistently, you will do well. But there will almost certainly be some gamblers who will do better, maybe much better, than you—through sheer chance. There’s nothing to be gained from envying, glorifying, copying, or studying such outcomes. Business dynamics are probabilistic, and outcomes are subject to randomness. That’s the reality of how things work. Hard as it may be to stomach. Though its tools may look simple, probabilistic thinking is an incredibly powerful concept, central to nearly every aspect of business reasoning and managerial decision making. WIN = When It’s Non-Linear Sometimes you may think you have the right probabilistic framework. But that turns out to be dangerously wrong. This happens when one tries to apply “linear” thinking to “non-linear” problems. The math concepts in this section may seem confusing (they were for me too). But they lead to a simple takeaway: If your work involves capital or resource allocation decisions—such as project or venture financing, M&A, marketing channel spend, etc.—it’s worth getting intuitively familiar with the Kelly Criterion. Read below for why. Say I offered you this deal: – You start with $100. – We toss a coin. – Heads, your wealth grows by 50%. $100 multiplied by 1.5x = $150. – Tails, your wealth declines by 40%. $100 multiplied by 0.6x = $60. – Now we do it again: Same setup, but starting with either $150 or $60 based on the outcome of the first round. And repeat a million times. Each time using the value at the end of the prior round as the starting point for the next. Do you like this offer? At first glance, it looks good. Take a simple unit $1. There are equal 50% chances of getting to $1.50 and $0.60. So, the expected value = 50% * $1.50 + 50% * $0.60 = $1.05. A 5% expected gain. That looks like an edge in your favor. And if you keep playing, this edge should deliver a nice long-term return. Right? Wrong. Physics Nobel laureate Murray Gell-Mann and his colleague Ole Peters showed that while the average outcome for millions of theoretical players playing this game is indeed positive, any individual single player goes bust with near 100% certainty. What looks good for the theoretical average population will bankrupt you personally. If you don’t believe it, watch Peters’s demonstration here. The above illustrates a powerful practical result: In some situations, the theoretical average outcome over a hypothetical population (an “ensemble”), may be very different than the actual expected outcome for any individual person in that same population. This can feel uncomfortably counterintuitive. That’s because our natural instincts tend to be trained on arithmetic problems, like the simple Oil Baron game above, where the score at the next round is the current score plus or minus something. But many real-life problems are multiplicative in nature, like this coin toss game where the score at the next round is actually the current score multiplied or divided by something. Using arithmetic analysis tools for multiplicative processes is dangerously wrong. Unlike their arithmetic counterparts, multiplicative outcomes are subject to the “wildness” of exponential compounding or decay. (E.g., our game above is governed by a concept called its geometric mean, which is less than one, predicting decay.) Practitioners in areas like signal processing, information theory, operations management, and capital allocation are familiar with the above dynamic. And they have a powerful math tool in their arsenal to deal with it: the aforementioned Kelly Criterion. Perhaps the best simple introduction to it is Fortune’s Formula, which tells the story of mathematicians like John Kelly, Claude Shannon, and Ed Thorp. Their work helped transform decision-heuristics in industries ranging from information-technology to investment-management (not to mention blackjack and poker). Kelly-thinking is this: To maximize long-term growth rates, one must smartly size bets. Kelly’s math optimally sizes them to avoid the risk of game-over strikeouts, while still swinging for home-runs on the juicy pitches in which you have a big edge over the odds. . . . Statistician Hans Rosling had an important message for us all: Our beautifully complex world cannot be understood by words alone, numbers must always be in the mix. The business world is no exception. However great their words may be, business leaders must also speak fluent math. Working with our powerful AI companions makes this skill more important than ever. Hopefully these simple “math words,” and the tools they represent, can help: TRY, DO, WIN.

The Case for Sharpening Your Math Skills in the Age of AI

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