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?
People make their own fates, and if enough of us make our fate to be space explorers, perhaps we can actually get some space exploration done.
Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. ... I have chosen the word βatomβ to signify these ultimate particles.
Biologically inspired materials could revolutionize materials science. People looking at spider silk and abalone shells are looking for new ways to make materials better, cheaper, and with less toxic byproducts.
In future, children won't perceive the stars as mere twinkling points of light: they'll learn that each is a 'Sun', orbited by planets fully as interesting as those in our Solar system.
Everything great in science and art is simple. What can be less complicated than the greatest discoveries of humanity - gravitation, the compass, the printing press, the steam engine, the electric telegraph?
Yet if anyone believes that the earth rotates, surely he will hold that its motion is natural, not violent.
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