In no other branch of mathematics is it so easy for experts to blunder as in probability theory.
Interpretation
Probability theory is prone to errors, even among experts.
Martin Gardner emphasizes the complexity and potential for miscalculation present in probability theory. Despite being a mathematical discipline, its reliance on interpretation and statistical inference can lead even seasoned mathematicians to make incorrect assumptions or mistakes, highlighting the inherent difficulties and misconceptions that can arise within this field.
In practice
In a lecture about statistics, I quoted Martin Gardner's insights on probability theory to illustrate its complexities.
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.
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.
A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?
The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily over time. Also, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily over time.
I think we need to move to the moons of Mars and learn how to control robots that are on the surface. It's not the impatient way of getting there, but Mars has been there a long time.
Scientists must venture outside their comfort zones to show the public how cool - and how important - their work really is.
'Frankenstein' did not invent the fear of science; the novel found its audience because it dramatized anxieties that already existed. Although popular entertainment can, over the long run, shape public perceptions, it becomes popular in the first place only if it addresses preexisting hopes, fears, and fascinations.
First you guess. Don't laugh, this is the most important step. Then you compute the consequences. Compare the consequences to experience. If it disagrees with experience, the guess is wrong. In that simple statement is the key to science. It doesn't matter how beautiful your guess is or how smart you are or what your name is. If it disagrees with experience, it's wrong. That's all there is to it.
It was strange, in a way, because there were no ideas involved in the laser that weren't already known by somebody 25 years before lasers were discovered. The ideas were all there; just, nobody put it together.
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