Mathematics is not only real, but it is the only reality.
Interpretation
Mathematics is a fundamental truth that underpins all aspects of reality.
This quote by Martin Gardner emphasizes the significance of mathematics as a discipline that reveals the true nature of reality. It suggests that mathematics is not merely a tool for calculations, but rather a universal language that describes the patterns and laws that govern the world around us, highlighting its vital role in understanding both the physical universe and abstract concepts.
In practice
In a lecture on the importance of mathematics in physics, one might refer to this quote to illustrate how core mathematical principles form the foundation of physical laws.
Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.
Debunking bad science should be constant obligation of the science community, even if it takes time away from serious research or seems to be a losing battle. One takes comfort from the fact there is no Gresham's laws in science. In the long run, good science drives out bad.
If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.
In no other branch of mathematics is it so easy for experts to blunder as in probability theory.
There are, and always have been, destructive pseudo-scientific notions linked to race and religion; these are the most widespread and damaging. Hopefully, educated people can succeed in shedding light into these areas of prejudice and ignorance, for as Voltaire once said: "Men will commit atrocities as long as they believe absurdities."
Modern science should indeed arouse in all of us a humility before the immensity of the unexplored and a tolerance for crazy hypotheses.
You need propellants to accelerate toward Mars, then to decelerate at Mars, again to re-accelerate from Mars to Earth, and finally to decelerate back at Earth. Accordingly, the mass of these required propellants, in short, drives our need for innovative launch vehicles.
There must be enormous numbers of planets around the stars in the many galaxies in our observable universe. We may be sure that wonderful things are happening on these planets that the human race never will observe.
In the material sciences these are and have been, and are most surely likely to continue to be heroic days.
Those who know that the consensus of many centuries has sanctioned the conception that the earth remains at rest in the middle of the heavens as its center, would, I reflected, regard it as an insane pronouncement if I made the opposite assertion that the earth moves.
If the experience of science teaches anything, it's that the world is very strange and surprising. The many revolutions in science have certainly shown that.
I venture to define science as a series of interconnected concepts and conceptual schemes arising from experiment and observation and fruitful of further experiments and observations. The test of a scientific theory is, I suggest, its fruitfulness.
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