I am writing here to encourage you to enjoy mathematics, to appreciate its beauty, and recognize its incredible potential in application. The following are many links and resources which I have found useful as well as inspiring. Subjects which have the same profundity and beauty as mathematics are few and far between, and to allow others to miss out on the humbling and world-expanding experiences available in the world of mathematics would be a regret of mine for a long time to come.
- “God may not play dice with the universe, but something strange is going on with the prime numbers.” -Carl Pomerance
- “A mathematician is a device for turning coffee into theorems.” -Alfréd Rényi
- “It is not enough to be in the right place at the right time. You should also have an open mind at the right time.” -Paul Erdős
One of the most important components of truly engaging with mathematics is to find others to engage with mathematics together.
Online Articles, Discussions, and Places of Wonder
These links provide a seemingly infinite amount of mathematical content. I recommend losing yourself in them.
- Quanta Magazine’s Math Section
- Math.StackExchange ordered by Votes
- MathOverflow sorted by Votes
- Elementary Short and Useful Proofs from MathOverflow
Blogs and Websites
These are websites and blogs I find enlightening and entertaining.
- How to Become a Pure Mathematician
- Math ∩ Programming
- Terence Tao’s What’s New
- Circles Sines and Signals
Short and Recommended Reads
- A Brief History of Elliptic Curves by Paul Hewitt
- A Mathematician’s Apology by G. H. Hardy
- A Mathematician’s Lament by Paul Lockhart
- Advice to a Young Mathematician
- Elliptic Curves from Mordell to Diophantus and Back by Ezra Brown and Bruce Myers
- List of Important Publications in Mathematics from Wikipedia
- Mathematical Knowledge: Internal, Social, and Cultural Aspects by Yuri Manin
- Missed Opportunities by Freeman Dyson
- On Proof and Progress in Mathematics by William Thurston
Learning mathematics requires time, effort, and resources. Of course mathematical content is available in books, in journals, and from professionals. However, Sci-Hub and other book-sharing projects like LibGen and BookZZ exist to help freely spread information and can be used at the reader’s discretion. Promisingly, open source books are beginning to become popular in mathematics. Time and Energy are not cheap, but if the cost of the information can be free, perhaps many more will be able to appreciate the beauty of mathematics.
It is my hope that by aggregating this content and material, the barrier of entry into mathematics is (perhaps by some $\epsilon > 0$) slightly lowered.