Advice to a Young Mathematician

I came across this article Advice to a Young Mathematician. I think that this is a very relevant read, even for the younger members of the community. The article starts off:

The most important thing that a young mathematician needs to learn is of course mathematics. However, it can also be very valuable to learn from the experiences of other mathematicians. The five contributors to this article were asked to draw on their experiences of math- ematical life and research, and to offer advice that they might have liked to receive when they were just setting out on their careers....


For this week, let's focus on Sir Michael Atiyah's writeup, with sections of Warning, Motivation, Psychology, Problems versus Theory, The Role of Curiosity, Examples, Proof, Strategy, Independence, Style.

What is the main takeaway that you had? What speak the loudest to you?

Note by Calvin Lin
4 years, 10 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

My takeaway was from "The Role of Curiosity". In it, he asks the questions of "When is a particular result true? Is that the best proof, or is there a more natural or elegant one? What is the most general context in which the result holds?"

To me, those are great leading questions to consider when reading through any solution (even your own). It helps you interpret the question in a deeper context, and even relate it to other problems that you have seen before.

In a bigger picture, I like the learning method of "asking more questions". I feel that the best way to stimulate thinking and discussion is to broaden my own perspective on the problem, and try and come up with another way to approach it. This is shown in some of my comments, in which I intentionally ask questions to get a member to state a certain answer. This is ultimately very rewarding, though it can be frustrating initially.

Calvin Lin Staff - 4 years, 10 months ago

Log in to reply

"Only the mediocre are supremely confident of their ability. The better you are, the higher the standards you set yourself - you can see beyond your immediate reach." - Sir Michael Atiyah

Guilherme Dela Corte - 4 years, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...