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?
Unless a price can be put on carbon emissions that is high enough to force power companies and manufacturers to reduce their fossil-fuel use, there seems to be little chance of avoiding hugely damaging temperature increases
It is the desire for explanations that are at once systematic and controllable by factual evidence that generates science; and it is the organization and classification of knowledge on the basis of explanatory principles that is the distinctive goal of the sciences.
The reality is the majority of us will not get off this planet. So the long run is, some kind of space exploration has to benefit us here on Earth.
In the original introduction to the word meme in the last chapter of 'The Selfish Gene,' I did actually use the metaphor of a 'virus.' So when anybody talks about something going viral on the Internet, that is exactly what a meme is, and it looks as though the word has been appropriated for a subset of that.
In the Middle East, where populations are growing fast, the world is seeing the first collision between population growth and water supply at the regional level. For the first time in history, grain production is dropping in a geographic region with nothing in sight to arrest the decline. Each day now brings 10,000 more people to feed and less irrigation water with which to feed them.
Science seeks the truth. And it does not discriminate. For better or worse it finds things out. Science is humble. It knows what it knows and it knows what it doesn’t know. It bases its conclusions and beliefs on hard evidence -- evidence that is constantly updated and upgraded. It doesn’t get offended when new facts come along. It embraces the body of knowledge. It doesn’t hold on to medieval practices because they are tradition.
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