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I am just like 99% of my friends in France, who say on their resume they can speak fluent English. In reality, they can't even count up to three.

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Keith Devlin

What is mathematics? Ask this question of person chosen at random, and you are likely to receive the answer "Mathematics is the study of number. " With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers. " But that is about as far as you will get. And with that you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!

Answer, Come, Mathematics, Mean, Numbers, Years
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Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence.

Beauty, Depth, Depths, Essence, Like, Skins

Just as music comes alive in the performance of it, the same is true of mathematics. The symbols on the page have no more to do with mathematics than the notes on a page of music. They simply represent the experience.

Alive, Math, Notes, Pages, Same, True

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.

Arise, Education, Presented, Real, School

I certainly do care about measuring educational results. But what is an 'educational result?' The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need.

Care, Educational, Eye, Eyes, Result, Science

A PhD in Mathematics is three years of guessing it wrong, plus one week of getting it right and writing a dissertation.

Three, Week, Writing, Wrong, Years
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