Candidates for quantitative jobs — like those on Wall Street or in Silicon Valley — are sometimes asked offbeat questions such as: How many Ping-Pong balls fit in a 747? Called Fermi problems, these questions are not meant to elicit a precisely correct answer but rather to test an interviewee’s reasoning ability. The candidates must use mathematical relationships of scale and dimension to arrive at a reasonable guess: If the volume of a Ping-Pong ball is roughly X and that of the airplane roughly Y, then the sought-after quantity is Y divided by X. The problems enforce the basic discipline of combining what is known and observable with rigid mathematics to make sensible statements about the unknown or the unobservable.
In the past year, President Trump and members of his administration have shown that they would fail miserably in such interviews. Many administrations boast about their successes and perhaps exaggerate. But Mr. Trump and others have made quantitative claims that stretch not only the bounds of factual truth but of mathematical possibility.
In his State of the Union address on Tuesday evening, Mr. Trump repeated a claim the administration has made before: that prescription drug prices have been reduced by as much as 600 percent. On its face, a 600 percent reduction in drug prices would require a pharmaceutical company to pay you five times over to take a medication. Commerce Secretary Howard Lutnick has previously partially defended the claim by saying the percentage reduction is measured relative to the final price rather than the initial one; so going from $100 to $25 would represent a 300 percent price reduction. But that is not what those words mean. When President Joe Biden’s Inflation Reduction Act of 2022 resulted in a 79 percent decrease in some prescription drug costs, would the Trump administration have wanted to frame that achievement as a 376 percent reduction?
Attorney General Pam Bondi has claimed that the administration’s fentanyl seizures have saved 119 million American lives (later revised to 258 million), a number that would represent a plague on par with the Black Death. Mr. Trump has claimed that his tariffs and other efforts have generated $18 trillion of new investments in the United States — more than half the country’s gross domestic product — which would represent a rate of economic growth that dwarfed even the greatest periods of post-World War II expansion. It doesn’t take a policy expert to fact-check these statements. Elementary number sense and some understanding of the world reveal that these numbers are grossly out of scale.
These claims mark an escalation in the use of statistics as rhetorical decoration rather than as support for arguments constrained by shared rules. From the perspective of a math educator, this is not a minor abuse of statistics but a failure of epistemic responsibility, one that undermines the possibility of public reasoning itself.
Mr. Trump’s claims do not invite debate; they short-circuit it. Why even bother arguing with a recent claim by Mr. Trump’s Department of Homeland Security implying that it could deport 100 million people, approximately double the total number of immigrants in the entire country? These numbers go beyond plausibly being true to being inconsistent with known mathematical axioms and definitions.
One of the most striking things about the world of mathematics is the frequency with which people have their minds changed by persuasive arguments. I see this every day in my classroom. This is why innumeracy in public life matters even when dishonesty is expected. Mathematics education is valuable not only because it prepares people for technical jobs but because it helps to cultivate a more basic civic capacity. Students learn that numbers impose constraints that are nonnegotiable, that definitions must be attended to carefully and that claims must yield when sufficient reasoning shows they cannot be true. The definition of a prime number is the same for me as it was for Euclid, and 2,047 will never be a prime no matter how much I desire it.
Those habits of thinking — humility before evidence, respect for shared definitions and a willingness to revise — are what can make disagreement productive rather than insurmountable. When leaders abandon them, numbers lose their power to clarify and instead become cudgels to use against opponents, leaving the public without a common basis to judge competing claims.
We can and must hold our political leaders to a higher standard. When officials use absurd numbers, it shows that they believe that Americans are incapable of critiquing them. After the Trump era is over, much will be said about the lasting damage it has done to civic discourse. In addition to other reforms and acts of reconciliation, repairs will need to be made to the ways we engage in public argumentation and decision-making, particularly in the use of statistics. Before we can disagree productively, we must reach a common faith that some truths exist and are capable of being discovered. Perhaps a refresher course in basic math could be a fruitful place for everyone to start.
Aubrey Clayton is a teaching assistant in the Harvard University department of mathematics and an instructor in the division of continuing education.
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