To become a good mathematician, you need to love and apply this science more often in practice. Many mathematicians like to apply analytical methods of judgment in everyday life, using their scientific knowledge.
If you really decide to be a good mathematician, you should like this science. All mathematicians understand the beauty of this science, which is that with a certain set of mathematical tools at hand, you can solve a huge number of different problems, both purely theoretical and practical. If you are a novice mathematician, you need to develop a capacity for abstract thinking. It will be difficult to do this, try, for example, to imagine the geometric and physical meanings of different theorems.
Use math in practice, look for it in everything. Many everyday tasks that seem to be far from any scientific problem are easily solved with the help of a mathematical apparatus. Such problems are very common, for example, when you are renovating an apartment, working on a garden plot or trying to solve a problem in the workplace. Some mathematical formulas that have been studied at school have unexpected applications in practice, for example, you can calculate the length of a material wrapped in a tight roll using arithmetic sequences. However, there are many ways to solve such problems.
Look for like-minded people who are passionate about math. Make friends with them and share your experiences. Communicating with other mathematicians will give you a lot of new things, you will find more and more methods to solve problems. You will also know how much you lag behind or outperform others in math.
If you are studying at a school, university or other educational institution, keep up to date with all math related events. Take part in all maths Olympiads and discuss them with your fellow students. Try to be in competition with your classmates and how to get k-5 math. At the same time, always be prepared to learn something new from them.
Look for your own ways of proving and solving these or those theories and problems. Many international math competitions and Olympiads abound in all kinds of problems that require non-standard solutions from participants. Explore the tasks of past competitions and the solutions that have been proposed. Try to solve these problems on your own.
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I don’t call myself a good mathematician, but I can say that the previous answer is completely absurd. Because I know a lot of good mathematicians, and they’re all very different.
First of all, about what to do from childhood. I have a friend, a round orphan. He defended himself when he was 27. And he started math at 24. Alexander Grotendik really took up mathematics at 18, and became the greatest mathematician of the twentieth century, without which modern mathematics is impossible to imagine. Such cases.
Very often those who win at Olympiads become accomplished mathematicians. But not all good mathematicians are olympiads. I must say, you don’t even have to be an excellent student at university – I have such friends.
Finally, most mathematicians, including Fieldsey and Abel laureates, are married. The already mentioned Alexander Grotendik and Paul Erdosh are rather exceptions. Turing was a homosexual, so he couldn’t marry under those conditions. Some mathematicians – such as René Descartes or Alain Conne – never married, but were not squeamish about women either. But Gauss, Riemann, Cantor, Hilbert, Hirzebruch, Quillen, Faltins – get them – were married.
It takes fearlessness to be a good mathematician. You must not be afraid to solve the problem. Don’t be afraid to solve the problem. Don’t be afraid to look at the problem from an unexpected angle. Don’t be afraid that it won’t work. Don’t be afraid that a mistake will pop out in the same way as if it had worked – and it will! – and try again, in a different way.
To be a good mathematician – you have to accept the feeling of your own stupidity. By knowing that you don’t understand something trivial.
To become a good math grade 3 – you need patience. Because you have to consider all your options. Because you have to find a mistake – see above. You have to find all the mistakes.
To be a good mathematician, you need a bright head. But you can do it without it if you have fearlessness, humility and patience.
If to say all this in short, we have such a saying: “A mathematician lives for the sake of that brief moment of happiness, when he has already proved the result, and has not yet found a mistake in proving”. If you’re willing to live for that moment, then you have a good chance.
Push, and it’ll open up.
P.S. I had to leave professional math – partly because of laziness, partly because of too high demands on myself – but I did not stop doing it, I still write articles. Because there are no former mathematicians – especially in today’s world, when, thanks to the Internet, more and more new and most of the old articles are available, if not directly, through a friend, and in fact any mathematician. I live for that very short moment of happiness, because it is worth it.