“One cannot really argue with a mathematical theorem.”
- January 8, 1942 – March 14, 2018
- British
- Theoretical physicist, science writer
- Announced the black hole singularity theorem and Hawking radiation, and contributed to the popularization of science with his book “Talking about the Universe”
Quote
“One cannot really argue with a mathematical theorem.”
Explanation
In this quote, Stephen Hawking highlights the absolute certainty and logical rigor of mathematical theorems. A mathematical theorem, once proven, is considered undeniably true within its defined system. Unlike many aspects of scientific theory or philosophy, which are open to debate and reinterpretation, a properly derived theorem in mathematics has a level of certainty that makes it essentially immune to dispute. This is because mathematical reasoning is based on logical deduction and follows strict rules of proof, leaving no room for subjective interpretation or disagreement.
For instance, Pythagoras’ theorem—which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides—has been rigorously proven and remains valid in Euclidean geometry, regardless of personal opinion. Similarly, Fermat’s Last Theorem, which was famously unsolved for centuries, once it was proven by Andrew Wiles in 1994, became an unassailable truth within the world of mathematics. This level of certainty is what sets mathematics apart from the empirical sciences, where theories must often be revised or discarded in light of new experimental evidence.
Hawking’s point about the immovable nature of mathematical theorems is particularly relevant in the context of his own work in theoretical physics. In physics, mathematical models and equations are the tools that allow scientists to describe and predict the behavior of physical systems. However, unlike mathematical theorems, many physical theories are subject to empirical verification. They are always open to revision as new data or observations come in. In contrast, a mathematical result once proven holds a timeless and universal truth—a quality that makes mathematics the foundation of much scientific reasoning, even though its conclusions might not always be directly observable in the physical world.
