Solved Problems In Mathematics

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The long-term goal is to increase your understanding of a subject.

A good rule of thumb is that if you cannot adequately explain the solution of a problem to a classmate, then you haven’t really understood the solution yourself, and you may need to think about the problem more (for instance, by covering up the solution and trying it again).

译文url: My name is Leif and I wanted to ask you on your opinion on something-forgive me if this seems strange or random.

As someone who has apparently fit the profile of “child prodigy” and “genius” (e.g.

the fact that you graduated high school and university and earned your doctorate so young), I’m wondering if you think you possess something that only a few others have in terms of intellectual ability or not.

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I have always believed that if someone applies himself and puts in enough time, effort, concentration, and perseverance they can accomplish whatever they set their mind to.In math, contradiction is one type of proof in which you assume that the "thing" you want to prove is untrue and then show how the results of this assumption are just not possible.Atiyah, 89, has made major contributions to math and physics, winning top mathematics awards — the Fields Medal in 1966 and the Abel Prize in 2004.In other words, you couldn't figure out when the next prime number occurs by knowing some pattern.[The 11 Most Beautiful Mathematical Equations]However, Riemann saw that the frequency of prime numbers apparently closely follows one equation that became known as the Riemann Zeta function, according to the Clay Mathematics Institute.For related reasons, one should value partial progress on a problem as being a stepping stone to a complete solution (and also as an important way to deepen one’s understanding of the subject). Note: My English is quite poor, you may experience this in the solution.See also Eric Schechter’s “Common errors in undergraduate mathematics“. Hi, Not to be rude, but a translation of Descartes that captures the original poetry of his phrase better might be: Each truth I discovered was a rule that then served to discover other truths.But in recent years he has also put forth some mathematical proofs that didn't hold up — and now many of his colleagues are critical of his new claims and say they're unlikely to hold true, according to Science."The proof just stacks one impressive claim on top of another without any connecting argument or real substantiation," John Baez, a mathematical physicist at the University of California, Riverside, told Science.In his talk, Atiyah described the many, many times people have claimed to have proved the hypothesis, only to be proven wrong.I find that “playing” with a problem, even after you have solved it, is very helpful for understanding the underlying mechanism of the solution better.For instance, one can try removing some hypotheses, or trying to prove a stronger conclusion. It’s also best to keep in mind that obtaining a solution is only the short-term goal of solving a mathematical problem.


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