Long-time Slashdot reader fahrbot-bot shares a story that all started with a high school student’s innocuous question on TikTok, leading academic mathematicians and philosophers to weigh in on “a very ancient and unresolved debate in the philosophy of science,” reports Smithsonian magazine.
Is it invented, or discovered? And are the things that mathematicians work with — numbers, algebraic equations, geometry, theorems and so on — real? Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered — a position known as Platonism…. Many mathematicians seem to support this view. The things they’ve discovered over the centuries — that there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on forever — seem to be eternal truths, independent of the minds that found them….
Other scholars — especially those working in other branches of science — view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago. Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all…?
Platonism has various alternatives. One popular view is that mathematics is merely a set of rules, built up from a set of initial assumptions — what mathematicians call axioms… But this view has its own problems. If mathematics is just something we dream up from within our own heads, why should it “fit” so well with what we observe in nature…? Theoretical physicist Eugene Wigner highlighted this issue in a famous 1960 essay titled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Wigner concluded that the usefulness of mathematics in tackling problems in physics “is a wonderful gift which we neither understand nor deserve.”