Famous Algebra Quotes

Arabs used to produce science and algebra and now we’re famous for killing.

There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward. When you’re asked to solve

Where would tourism be without a little luxury and a taste of night life? There were several cities on Deanna, all moderate in size, but the largest was the capital, Atro City. For the connoisseur of fast-foods, Albrechts’ famous hotdogs and coldcats were sold fresh from his stall (Albrecht’s Takeaways) on Lupini Square. For the sake of his own mental health he had temporarily removed Hot Stuff Blend from the menu. The city was home to Atro City University, which taught everything from algebra and make-up application to advanced stamp collecting; and it was also home to the planet-famous bounty hunter – Beck the Badfeller. Beck was a legend in his own lifetime. If Deanna had any folklore, then Beck the Badfeller was one of its main features. He was the local version of Robin Hood, the Davy Crockett of Deanna. The Local rumor mill had it he was so good he could find the missing day in a leap year. Once, so the story goes, he even found a missing sock.

Albert Einstein, considered the most influential person of the 20th century, was four years old before he could speak and seven before he could read. His parents thought he was retarded. He spoke haltingly until age nine. He was advised by a teacher to drop out of grade school: “You’ll never amount to anything, Einstein.” Isaac Newton, the scientist who invented modern-day physics, did poorly in math. Patricia Polacco, a prolific children’s author and illustrator, didn’t learn to read until she was 14. Henry Ford, who developed the famous Model-T car and started Ford Motor Company, barely made it through high school. Lucille Ball, famous comedian and star of I Love Lucy, was once dismissed from drama school for being too quiet and shy. Pablo Picasso, one of the great artists of all time, was pulled out of school at age 10 because he was doing so poorly. A tutor hired by Pablo’s father gave up on Pablo. Ludwig van Beethoven was one of the world’s great composers. His music teacher once said of him, “As a composer, he is hopeless.” Wernher von Braun, the world-renowned mathematician, flunked ninth-grade algebra. Agatha Christie, the world’s best-known mystery writer and all-time bestselling author other than William Shakespeare of any genre, struggled to learn to read because of dyslexia. Winston Churchill, famous English prime minister, failed the sixth grade.

There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward.

And one of the things that has most obstructed the path of discipleship in our Christian culture today is this idea that it will be a terribly difficult thing that will certainly ruin your life. A typical and often-told story in Christian circles is of those who have refused to surrender their lives to God for fear he would “send them to Africa as missionaries.” And here is the whole point of the much misunderstood teachings of Luke 14. There Jesus famously says one must “hate” all their family members and their own life also, must take their cross, and must forsake all they own, or they “cannot be my disciple” (Luke 14:26–27, 33). The entire point of this passage is that as long as one thinks anything may really be more valuable than fellowship with Jesus in his kingdom, one cannot learn from him. People who have not gotten the basic facts about their life straight will therefore not do the things that make learning from Jesus possible and will never be able to understand the basic points in the lessons to be learned. It is like a mathematics teacher in high school who might say to a student, “Verily, verily I say unto thee, except thou canst do decimals and fractions, thou canst in no wise do algebra.” It is not that the teacher will not allow you to do algebra because you are a bad person; you just won’t be able to do basic algebra if you are not in command of decimals and fractions. So this counting of the cost is not a moaning and groaning session. “Oh how terrible it is that I have to value all of my ‘wonderful’ things (which are probably making life miserable and hopeless anyway) less than I do living in the kingdom! How terrible that I must be prepared to actually surrender them should that be called for!” The counting of the cost is to bring us to the point of clarity and decisiveness. It is to help us to see. Counting the cost is precisely what the man with the pearl and the hidden treasure did. Out of it came their decisiveness and joy. It is decisiveness and joy that are the outcomes of the counting.

One thing that we conclude from all this is that the 'learning robot' procedure for doing mathematics is not the procedure that actually underlies human understanding of mathematics. In any case, such bottom-up-dominated procedure would appear to be hopelessly bad for any practical proposal for the construction of a mathematics-performing robot, even one having no pretensions whatever for simulating the actual understandings possessed by a human mathematician. As stated earlier, bottom-up learning procedures by themselves are not effective for the unassailable establishing of mathematical truths. If one is to envisage some computational system for producing unassailable mathematical results, it would be far more efficient to have the system constructed according to top-down principles (at least as regards the 'unassailable' aspects of its assertions; for exploratory purposes, bottom-up procedures might well be appropriate). The soundness and effectiveness of these top-down procedures would have to be part of the initial human input, where human understanding an insight provide the necesssary additional ingredients that pure computation is unable to achieve. In fact, computers are not infrequently employed in mathematical arguments, nowadays, in this kind of way. The most famous example was the computer-assisted proof, by Kenneth Appel and Wolfgang Haken, of the four-colour theorem, as referred to above. The role of the computer, in this case, was to carry out a clearly specified computation that ran through a very large but finite number of alternative possibilities, the elimination of which had been shown (by the human mathematicians) to lead to a general proof of the needed result. There are other examples of such computer-assisted proofs and nowadays complicated algebra, in addition to numerical computation, is frequently carried out by computer. Again it is human understanding that has supplied the rules and it is a strictly top-down action that governs the computer's activity.