Home / Quotes / Quote by Leonhard Euler

Quote by Leonhard Euler

“Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived - namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken - has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.”

Quote by Leonhard Euler

Author

Leonhard Euler was a Swiss mathematician who made significant contributions to mathematics, physics, and engineering. He was born on April 15, 1707, and died on September 18, 1783. Euler's work covered a wide range of mathematical branches, from calculus to number theory, and his publications had a profound impact on posterity. more

You May Also Like

“The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such a discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful.”

Should Kind May Use Care Opportunity Numbers Education Accepting Cases Prove Discovery Mathematics Property Errors Mere Math Observation Distinguished Euler

Author:Leonhard Euler

“A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some "dreaming" time.”

Should Problem Dream Challenges Education Students Exercise Mathematics Mere Math

Author:Howard Whitley Eves

“Imagine that you wanted your children to learn the names of all their cousins, aunts and uncles. But you never actually let them meet or play with them. You just showed them pictures of them, and told them to memorize their names. Each day you'd have them recite the names, over and over again. You'd say, "OK, this is a picture of your great-aunt Beatrice. Her husband was your great-uncle Earnie. They had three children, your uncles Harpo, Zeppo, and Gummo. Harpo married your aunt Leonie ... yadda, yadda, yadda."”

Children Play Wanted Three Names Education Imagine Husband Married Our Children Mathematics Your Children Each Day Imagine That Uncles Cousin Aunt Aunts And Uncles Great Aunt

Author:Brian X. Foley

“In no other branch of mathematics is it so easy for experts to blunder as in probability theory.”

Easy Education Theory Mathematics Math Experts Branches Probability Blunders Probability Theory

Author:Martin Gardner

“Indeed, there is something to be said for the old math when taught by a poorly trained teacher. He can, at least, get across the fundamental rules of calculation without too much confusion. The same teacher trying to teach new math is apt to get across nothing at all.”

Trying Said Education Teach Too Much Teacher Taught Mathematics Fundamentals Math Confusion Calculations

Author:Martin Gardner

“The toughest thing for a homeschooler is the same as for a school teacher - shifting from a weak tea vision of math being grinding calculations to a rich frothy mug of math as an active way of thinking.”

Thinking Way School Education Vision Rich Teacher Weak Mathematics Active Math Tea Shifting Way Of Thinking Calculations School Teachers Mug

Author:John Golden

“The ultimate goal of mathematics is to eliminate all need for intelligent thought.”

Needs Goal Education Ultimate Intelligent Mathematics Math Ultimate Goal

Author:Ronald Graham

“Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.”

Said Remember Courses Education Teacher Students Materials Amount Concerned Mathematics Sticks Average Math Things To Do Formulas Cynic

Author:Paul Halmos

“To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.”

Facts Christian Belief Education Mathematics Math Theology Mathematical Branches Math Education Numbers And Math

Author:Hilda Phoebe Hudson

“...the science of calculation also is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not be in indulged in by one who is to have a profession to follow for his subsistence.”

Source: Jefferson: Writings