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?
There are no black holes in the sense of regimes from which light can't escape to infinity.
There are as many species as the infinite being created diverse forms in the beginning, which, following the laws of generation, produced many others, but always similar to them: therefore there are as many species as we have different structures before us today.
The more I work with the powers of Nature, the more I feel God's benevolence to man; the closer I am to the great truth that everything is dependent on the Eternal Creator and Sustainer; the more I feel that the so-called science, I am occupied with, is nothing but an expression of the Supreme Will, which aims at bringing people closer to each other in order to help them better understand and improve themselves.
Science has helped us to understand and master ourselves, creating an elevated new form of human life, the wealth and beauty of which cannot be pictured today by the keenest imagination.
Most people are excited about themselves. Personal genome will deliver for inexpensively something about science to which you can relate. Just like computers are becoming something to which you can relate. It should be even easier to relate to your own biology, and I hope that will be one of the ways we get broader literacy in science.
There is no example of someone reading their scripture and saying, 'I have a prediction about the world that no one knows yet, because this gave me insight. Let's go test that prediction,' and have the prediction be correct.
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