Start where you are at, and don’t compare yourself to others. Work hard, get help, and stay on the path. Sometimes you will fail. That’s OK. Enjoy what you are doing now, and don’t forget to play, mathematically and otherwise. Do lots of calculations and examples, be curious, be solid on the basics. Also, remember to take care of yourself. Take one day a week off work. Sleep well and exercise. Have a social life.
fresh_42 said:Here's an interview I've found on the AMS site, which I think offers some interesting insights on the way to become a scientists.
http://www.ams.org/publications/journals/notices/201707/rnoti-p718.pdf
Especially what she said about the learning process can be seen as a real good advice:
Karen E. Smith became interested in mathematics at a young age, as she always enjoyed solving puzzles and problems. She also had a strong math teacher in high school who encouraged her to pursue the subject.
Karen E. Smith's research focuses on commutative algebra and algebraic geometry. She is particularly interested in studying the behavior of algebraic equations and their solutions.
Karen E. Smith has made several significant contributions to mathematics, including co-authoring the book "An Invitation to Algebraic Geometry" and publishing numerous research papers in top journals. She has also won several awards and honors for her work.
Karen E. Smith advises young mathematicians to not be afraid to ask questions and seek help when needed. She also encourages them to be persistent and not give up when faced with challenges.
Karen E. Smith believes in maintaining a healthy work-life balance and makes sure to prioritize her family and personal life. She also enjoys hiking and spending time outdoors as a way to relax and recharge.