The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.
Interpretation
John Stuart Mill praises the impact of algebra on geometry and its significance in the development of exact sciences.
In this quote, John Stuart Mill highlights how the integration of algebraic principles into geometry fundamentally transformed the study of mathematics and paved the way for advancements in the sciences. He attributes immense importance to this intellectual leap made by René Descartes, suggesting that it has fundamentally altered our understanding of the exact sciences, representing a monumental step in scientific progress.
In practice
In a lecture about the history of mathematics, one might use this quote to illustrate the importance of Descartes' contributions.
The peculiar evil of silencing the expression of an opinion is, that it is robbing the human race; posterity as well as the existing generation; those who dissent from the opinion, still more than those who hold it. If the opinion is right, they are deprived of the opportunity of exchanging error for truth: if wrong, they lose, what is almost as great a benefit, the clearer perception and livelier impression of truth, produced by its collision with error.
As for charity, it is a matter in which the immediate effect on the persons directly concerned, and the ultimate consequence to the general good, are apt to be at complete war with one another.
To think that because those who wield power in society wield in the end that of government, therefore it is of no use to attempt to influence the constitution of the government by acting on opinion, is to forget that opinion is itself one of the greatest active social forces. One person with a belief is a social power equal to ninety-nine who have only interests.
There should be perfect freedom, legal and social, to do the action and stand the consequences. It would be a great misunderstanding of this doctrine to suppose that it is one of selfish indifference, which pretends that human beings have no business with each other's conduct in life, and that they should not concern themselves about the well-doing or well-being of one another, unless their own interest is involved.
Political Economy, in truth, has never pretended to give advice to mankind with no lights but its own; though people who knew nothing but political economy (and therefore knew it ill) have taken upon themselves to advise, and could only do so by such lights as they had.
Marriage is the only actual bondage known to our law. There remain no legal slaves, except the mistress of every house.
A theory should not attempt to explain all the facts, because some of the facts are wrong
...great difficulties are felt at first and these cannot be overcome except by starting from experiments .. and then be conceiving certain hypotheses ... But even so, very much hard work remains to be done and one needs not only great perspicacity but often a degree of good fortune.
What we can be scientifically certain of is that our continued use of fossil fuels is pushing us to a point of no return
The search for knowledge is in our genes. It was put there by our distant ancestors who spread across the world, and it's never going to be quenched.
Rising carbon price is essential to 'decarbonize' the economy - to remove the nation towards the era beyond fossil fuels.
Given the power and influence that science increasingly has in our daily lives, it is important that we as citizens of an open and democratic society learn to separate good science from bunk. This is not just a matter of intellectual curiosity, as it affects where large portions of our tax money go, and in some cases even whether people’s lives are lost as a result of nonsense.
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