La théorie des séries infinies en général est justqu’à présent très mal fondée. On applique aux séries infinies toutes les opérations, come si elles aient finies; mais cela est-il bien permis? Je crois que non. Où est-il démonstré qu/on ontient la différentielle dune série infinie en prenant la différentiaella de chaque terme. Rien n’est plus facile que de donner des exemples où cela n’est pas juste.
Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.

A minor operation: one performed on somebody else.

All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

Even a good operation done poorly is still a poor operation.

Exploratory operation: a remunerative reconnaissance.

Having made a sufficient opening to admit my finger into the abdomen, I passed it between the intestines to the spine, and felt the aorta greatly enlarged, and beating with excessive force. By means of my finger nail, I scratched through the peritoneum on the left side of the aorta, and then gradually passed my finger between the aorta and the spine, and again penetrated the peritoneum, on the right side of the aorta. I had now my finger under the artery, and by its side I conveyed the blunt aneurismal needle, armed with a single ligature behind it...
Describing the first ligation of the aorta in 1817 for left femoral aneurysm.

I find that most men would rather have their bellies opened for five hundred dollars than have a tooth pulled for five.

It is not therefore the business of philosophy, in our present situation in the universe, to attempt to take in at once, in one view, the whole scheme of nature; but to extend, with great care and circumspection, our knowledge, by just steps, from sensible things, as far as our observations or reasonings from them will carry us, in our enquiries concerning either the greater motions and operations of nature, or her more subtile and hidden works. In this way Sir Isaac Newton proceeded in his discoveries.

It takes five years to learn when to operate and twenty years to learn when not to.

Medicine has made all its progress during the past fifty years. ... How many operations that are now in use were known fifty years ago?—they were not operations, they were executions.

My lectures were highly esteemed, but I am of opinion my operations rather kept down my practice, than increased it.

The power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.