每日科技报告 4月25日 10 Great Minds Every Math Student Should Know

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10 Great Minds Every Math Student Should Know

The work of mathematical geniuses can inspire intimidation or even fear into the hearts of aspiring students. And who can blame them? Often given a barrage of principles and functions with little to no real-world application offered, it's no wonder why so many students, math majors and non-majors alike, have such trouble wrapping their minds around mathematical ideas that originated centuries ago. Rarely will a math class ever provide any sort of context to the mathematical concepts taught beyond the concepts themselves. Rarely will students ever receive an insight into the person who created the idea. Sure, it may not solve all math woes, but it could definitely help foster a better understanding of so many students' least favorite subject.

• Sir Isaac Newton, 1643-1727: Perhaps the greatest of all mathematical minds, Newton originated several mathematical and scientific principles which changed the way people viewed the universe. His most commonly known achievement would have to be his Principia, which paved the way for classical mechanics, described universal gravitation, and described the three laws of motion. It was this work that dispelled any remaining doubts of the time, including the Catholic Church's, of the earth revolving around the sun. Sharing credit with Gottfried Leibniz, Newton developed differential and integral calculus, one of the most common causes of headache among adolescents and young adults. While Newton also created a good number of inventions and developed several advancements and many other fields of study (like optics), these gargantuan achievements in physics and mathematics originated a whole new standard of thinking about the universe that dominated thinking for about 300 years
• Paul Erdos, 1913-1996: Known as a "problem solver" rather than "theory developer," Erdos founded no new field of mathematics. However, he published more **s than any other mathematician in history, working with 511 different collaborators in his lifetime. Most notably, Erdos worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. Completely shattering the stereotype of the quiet, reserved nerd, Erdos led quite the unconventional life, resembling mostly that of a vagabond, traveling between scientific conferences and the homes of colleagues all over the world. He gave most of his awards and earnings to people in need an various worthy causes. Known for his eccentric personality and behavior, Erdos was known to drink copious amounts of coffee as well as to take amphetamines all for the purpose of increasing advancements in mathematics.
• Alan Turing, 1912-1954: Ever wonder how we got from the light bulb to that computer you're using? A large amount of credit must be given to Alan Turing who created the first detailed design of a stored-program computer. Highly influential in the development of computer science, Turing proved that a computational machine would be capable of performing any conceivable mathematical computation if it were representable as an algorithm. In some ways, Turing was way ahead of his time, creating a chess program so complex that there was no computer powerful enough at the time to execute it; nonetheless, Turing simulated the program himself. In addition to his developments in computer science, Turing was a phenomenal code-breaker and put these skills to work in World War II breaking German code.
• Henri Poincare, 1854-1912: Though the man supposedly flunked an IQ test, Poincare was one of the most creative mathematicians ever. He is sometimes called the Father of Topology, but he also produced large amounts of work in many areas of math including the theory of differential equations, foundations of homology, the theory of periodic orbits, and the discovery of automorphic functions. He also formulated the Poincare conjecture, one of the most famous problems in mathematics that remained unsolved for an entire century. In his research on the three-body problem (a problem that had eluded mathematicians since Newton's time), Poincare discovered a chaotic deterministic system which laid the foundations of modern chaos theory.
• Muhammad ibn Musa al-Khwarizmi, c. 780-c. 850: It's surprising sometimes how few people realize the Persian impact on mathematics. If it were not for al-Khwarizmi's work on Indian numerals, the Western world would have gotten the decimal positional number system much, much later. al-Khwarizmi wrote the first systematic solution of linear and quadratic equations in Arabic. Though once considered the original inventor of algebra, we now know that his work is based on older Greek and Indian sources. His contribution to both algebra and geometry were vital nonetheless. Essentially, al-Khwarizmi's work established the basis for innovation in algebra and trigonometry. In fact, the term algebra is derived from the name of one of the basic operations with equations (al-jabr, meaning completion, or, subtracting a number from both sides of the equation) described in his book.
• Pythagoras, c. 570 BC-c. 495 BC: Not only was Pythagoras credited as being the first to use axioms and deductive proofs (placing a huge influence on Plato and Euclid), he was perhaps the only mathematician to have rigorous, spiritual disciples, called Pythagoreans, who followed and extended his mathematical research. Interestingly, many of his results were supposedly due to his students though none of their writings survive. In light of the issue of crediting work, the Pythagoreans made so many advancements in mathematics, it almost doesn't matter. Discoveries include the Pythagorean Theorem, amicable numbers, polygonal numbers, golden ratio, the five regular solids, and irrational numbers. Also, the Pythagoreans were one of the few ancient schools to practice gender equality.
• Rene Descartes, 1596-1650: Although Descartes is often called the "Father of Modern Philosophy," he created quite a few influential advancements in the field of mathematics as well. The Cartesian coordinate system, which allowed geometric shapes to be expressed in algebraic equations, was named after him. Descartes's laid the foundation for the calculus of Newton and Leibniz by applying infinitesimal calculus to the tangent line problem. Descartes also created analytic geometry and an early form of the law of conservation of momentum. His rule of signs, which can determine the number of positive and negative roots of a polynomial, is still commonly used today.
• Leonhard Euler, 1707-1783: If you're having trouble understanding the notation for trigonometric functions, natural logarithms, or the function notation f(x), you can probably blame Euler. Often called the greatest mathematician of all time, Euler made important discoveries in fields as diverse as infinitesimal calculus and graph theory. Euler also introduced much of modern mathematical terminology and notation. Euler worked in about all areas of mathematics: geometry, infinitesimal calculus, trigonometry, algebra, and number theory. And that's not including his work in physics, in which he studied mechanics, fluid dynamics, optics, and astronomy. Euler was so prolific that his work output slowed very little despite the fact that he became blind later in life.
• Carl Friedrich Gauss, 1777-1855: Gauss first began displaying his brilliance in math at the age of three when he corrected his father's arithmetic. Known as "the Prince of Mathematics" Gauss began questioning the axioms of Euclid at age twelve, and at age 24, he published Disqueitiones Arithmeticae, arguably the greatest book of pure mathematics ever. Among Gauss's numerous contributions to mathematics are the first complete proof of Euclid's Funamental Theorem of Algebra (that an nth degree polynomial has n complex roots), hypergeometric series, foundations of statistics, and differential geometry. However being an stern perfectionist and hard worker, Gauss was never a prolific writer as he refused to publish work that he did not consider complete and above criticism.
• Thomas Bayes, 1702-1761: Can a man of God study numbers and probability? Bayes sure did. Both a theologian and a mathematician, Bayes was the first to use probability inductively. His work, "Essay Towards Solving a Problem in the Doctrine of Chances," laid down the basis of a statistical technique now called Bayesian probability, for calculating the probability of the validity of a proposition on the basis of a prior estimate and new relevant evidence. This is also known as inverse probability where essentially a probability is assigned a hypothesis and then tested and updated in the light of new data. Quite a progressive view on determinism for a Presbyterian minister in the 18th century.