Can we become mathematicians by self-study? (Part 3)

Before the question “should I become a mathematician or not” , the question is whether you love math with a passionate love, admiration and patience for math or not. If you love math, love it. If you like the idea of becoming a mathematician then you should establish a vision to make math your hobby. Once you have a vision, what knowledge do you need to equip to pursue a career in math?

Readers are invited to part 3, which is also the last part: the path to becoming a self-taught mathematician. The series summarizes the opinions of the readers of, one of the world’s leading Q&A websites.

Matthew Graham , a reader with a bachelor’s degree in math-statistics and a career in research, offers some very practical advice for math lovers like him.

Matthew graduated from Saint Louis University (Missouri) ranked 140th in the US and top 500 in the world in the Academic Rankings of World Universities 2018.

Can we become mathematicians by self-study? (Part 3)
Reader Matthew Graham, BA in Mathematics and Statistics from Saint Louis University, Missouri, USA

According to Matthew, to become a self-taught mathematician, you need to have conditions such as: budget to buy books, time (it takes a lot of time), determination and absolute patience, of which the main thing. The core is work ethic. And you have to be willing to spend many, many years of your life learning math, because that’s what you need to get to the level of a modern mathematician.

Matthew recommends the following subjects: start with basic subjects like elementary algebra, geometry, and trigonometry, then learn how to write proofs. After the above basic subjects are calculus, abstract algebra, complex variables.

Once you have a foundation, there are many paths for you to pursue such as differential equations, probability/statistics, combinatorics/graph theory, topology, etc.

Proving is an extremely basic skill in math, you can’t call yourself a mathematician without never having a proof. You need a very strong foundation for this demonstration skill, a skill whose importance cannot be fully expressed. Without basic trigonometry/algebra and proof writing skills, you won’t be a future mathematician. Read some good books on the subject.

For advanced math subjects, Matthew recommends several books and authors such as Michael Spivak’s book on integrals, abstract algebra by John B Fraleigh, David S. Dummit and Richard M. Foote, a book about complex variables is Visual Complex Analysis.

Integrating is not an easy challenge so you need to learn it slowly and surely. Good books will help you learn a lot and go at the right pace. This is not a race, all the above material is very difficult, go slow and steady to ensure mastery of the basic concepts. You don’t need to rush.

Can we become mathematicians by self-study? (Part 3)
In Matthew’s practical mind, being a self-taught mathematician is not possible these days. (Artwork: Fiverr)

The best option is to take classes at a local community college if you can. Online classes can also be effective, but it will still kick the math ball back entirely on you.

If you’re really after the book and field of study suggestions above, expect a year in each. You have to go slow and make sure you really understand everything in the book. Study only one section every two to three days and solve at least 20 problems for each section to consolidate and develop knowledge. Math Stackexchange, reddit and quora will be your companions in this.

In Matthew’s practical mind, being a self-taught mathematician is not possible these days. If you want to publish research without a PhD in math, forget it. Math courses are way too deep for you to simply pick them up after just reading through some research. You must learn the basics in each subject first!

And then there comes a time when you can no longer simply choose a textbook. Matthew had just graduated from college and was preparing for graduate school in math, so he couldn’t recommend any better graduate program books than the signature ones by Rudin, Munkres, Dummit, Foote.

In general, to become a mathematician, you need to explore relevant graduate research opportunities and be exposed to active areas of research . You simply cannot get there on your own in today’s world. You need guidance from an expert.

The Academic Rankings of World Universities (ARWU ) that we reference in this series is one of the three most influential and well-known university rankings in the world today, along with two of He is the QS World Universities Rankings and the Times Higher Education World Universities Rankings-THE. When it was first established in 2003, ARWU was compiled by Shanghai Jiaotong University (China). Since 2009 ARWU has been implemented and managed by Shanghai Ranking Consultancy, an independent institution of higher education. ARWU focuses on scientific research and academic achievement at the “elite” level—the highest level of research activity in universities: the number of Nobel laureates and Fields medalists. , the social science citation index and extension, the number of articles published in the journals Nature and Science…