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?
Science and fiction both begin with similar questions: What if? Why? How does it all work? But they focus on different areas of life on earth.
I can never look now at the Milky Way without wondering from which of those banked clouds of stars the emissaries are coming. If you will pardon so commonplace a simile, we have set off the fire alarm and have nothing to do but to wait. I do not think we will have to wait for long.
In more than one respect, the exploring of the Solar System and homesteading other worlds constitutes the beginning, much more than the end, of history.
Science is the tool of the Western mind and with it more doors can be opened than with bare hands.
To command their professors of astronomy to refute their own observations is to command them not to see what they do see and not to understand what they do understand.
You don't have money, you can't do science. But that's part of the price that I pay.
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