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.
It is foolish to claim, as some do, that emigration into space offers a long-term escape from Earth's problems. Nowhere in our solar system offers an environment even as clement as the Antarctic or the top of Everest.
A review of seventy-four clinical trials of antidepressants, for example, found that thirty-seven of thirty-eight positive studies [that praised the drugs] were published. But of the thirty-six negative studies, thirty-three were either not published or published in a form that conveyed a positive outcome.
The phenomena of nature, especially those that fall under the inspection of the astronomer, are to be viewed, not only with the usual attention to facts as they occur, but with the eye of reason and experience.
Whoever, in the pursuit of science, seeks after immediate practical utility, may generally rest assured that he will seek in vain.
Science is rooted in the will to truth. With the will to truth it stands or falls. Lower the standard even slightly and science becomes diseased at the core. Not only science, but man. The will to truth, pure and unadulterated, is among the essential conditions of his existence; if the standard is compromised he easily becomes a kind of tragic caricature of himself.
The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases.
Subscribe for the occasional hand-picked quote. No noise.