The Magical Maze
An entertaining philosophical introduction to mathematics; pop-sci, but (aside from its
title perhaps) not irritatingly so. It developed from a series of lectures that the
author gave. If you are looking for a popularization of mathematics in a book form,
for my money, you can't do much better than this. This is because it goes quite a bit
deeper than most, and it can do that because it uses the metaphor of a maze; and it
uses this metaphor to explore fundamental mathematical concepts such as proof and
computability - while at the same time, preventing things from getting too abstract
by motivating with many relatable examples, such as the Monty Hall problem.
Archimedes' Revenge
Compactness and Contradiction
Infinity - A simple, but not too simple introduction
Before you do any serious thinking about mathematics you should probably try to decide what
your feelings towards infinity are.
Practice of mathematics
Examples of common false beliefs in mathematics.
Math papers where the only issue is that someone else could\'ve done it but didn\'t
When has the scaffolding been more important than the completed building?
Big ideas that began small or small ideas that became big
Proofs of theorems that proved more or deeper results than what was first supposed or stated as the corresponding theorem
Every mathematician has only a few tricks
Poincaré on intuition in mathematics - MacTutor History of Mathematics
There's more to mathematics than rigour and proofs | What\'s new
Is an interpretation mathematics (fit for publication)?
Are hypergeometric series not taught often at universities nowadays, and if so, why?
Is there a reason it is so rare we can solve differential equations?
How many words (i.e. not \"math\" symbols\") should I use in my proofs?
Why do we have two theorems when one implies the other?
Theorems with many distinct proofs
\"Strange\" proofs of existence theorems
Studying mathematics
Why\'s math way more puzzling, abstruse than law and medicine?
Why there is no Hitchhiker's Guide to Mathematics for Programmers | Math ∩ Programming
How can I counter a student response saying \"Why are we bothered to reinvent the wheel when proving mathematical identities?\"
Response to Students Who Say \"This Is Not Important\"
Daunting papers/books and how to finally read them
Learning mathematics in an \"independent and idiosyncratic\" way
Mathematical Rigour
Why is writing down mathematical proofs more fault-proof than writing computer code?
Consequences of lack of rigour
Soft question: Examples where lack of mathematical rigour cause security breaches?
Controversy in mathematics
Replication crisis in mathematics
Titans of Mathematics Clash Over Epic Proof of ABC Conjecture | Quanta Magazine
The ABC conjecture has (still) not been proved | Persiflage
Notes on the Oxford IUT workshop by Brian Conrad | mathbabe
Endless controversy
Why are most cranks old men?
Paul du Bois-Reymond - Wikipedia
James Dugundji - Wikipedia
Can we define algebraic structures (group, rings, modules, fields) via their arrows?
If two pairs of numbers have equal sums and products, what can we conclude about the pairs?
Readings | Mathematics for Computer Science | Electrical Engineering and Computer Science | MIT OpenCourseWare