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So calculus, differential equations, and linear algebra have always been the most emphasized, and for good reason – these are very important. The standard high school curriculum traditionally has been focused towards physics and engineering.
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Ultimately you should follow advice not because someone tells you to, but because it was something that you already knew you should be doing. But unlike TV, we have to do the work ourselves to figure out what happens next.
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Research sometimes feels like an ongoing TV series in which some amazing revelations have already been made, but there are still plenty of cliff-hangers and unresolved plotlines that you want to see resolved. The accuracy of Wikipedia can be dodgy in some places, but in maths, it’s really quite good. Mathematical problems, or puzzles, are important to real mathematics (like solving real-life problems), just as fables, stories and anecdotes are important to the young in understanding real life. Volume grows spatially slower than scaling. I tend to change research direction every few years or so. There might be a hidden structure in pi that we simply haven’t discovered.
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I am a husband and a father and a proud citizen of two countries: my homeland of Australia and my adopted country here in the United States. In the 19th century, they taught spherical trigonometry because one of the biggest applications of mathematics was navigating the ocean. Math education has changed over the years. ~ Terence Tao.Įducation is a complex, multifaceted, and painstaking process, and being gifted does not make this less so. I remember having this vague idea that what mathematicians did was that some authority, someone, gave them problems to solve, and they just sort of solved them. I have been lucky to find very good collaborators who have taught me a lot, have introduced me to several new fields of mathematics, or have shown me new insights. People usually framed the cheque instead. It was traditional to not actually cash the prizes that Erdos did award while he was alive.
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Pointing out that countless great mathematicians had tried to solve the problem and failed before you came along is in particularly bad taste and should be avoided completely. When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed. I think one nice thing about mathematics is that we don’t really have one prize that dominates all the others, like the Nobel prizes. ~ Terence Tao.Īt a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate. I talk online or with a colleague, and I get interested, and I just follow where it leads. ~ Terence Tao.Ī lot of the math that I do, it’s not sort of premeditated. ~ Terence Tao.Ĭan you make fancy patterns of water that actually have some computation power? I’m betting that fluids are complex enough to do this. I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world. There is often a chance meeting, or something that I worked on 10 years ago suddenly becomes important again. I often don’t know what I’ll be working on next year or a year from now. If I experiment enough, I get a deeper understanding. I feel like I have to sit down and work out exactly what the problem is.
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If there is something that I should know how to do but don’t, it bugs me. They’re going to be engineers, statisticians – in many ways, that’s the more important mission of math education. Most students who take math classes aren’t going to be mathematicians. When you’re concentrating hard, hours can fly by, and it’s just you and a math problem. I look at a problem, play with it, work out a strategy. I am still very fond of Australia, but my life is now in Los Angeles.