Mathematics

(Up) | See also: FoM, Probability Theory, Combinatorics, Group Theory, Order Theory, Category Theory, Closure Systems, Topology, Matroid Theory, Numerical Analysis, Recreational Mathematics

---

Web resources

Practice of mathematics

Examples of common false beliefs in mathematics. - MathOverflow

soft question - Math papers where the only issue is that someone else could\'ve done it but didn\'t - MathOverflow

soft question - When has the scaffolding been more important than the completed building? - MathOverflow

soft question - Big ideas that began small or small ideas that became big - MathOverflow

reference request - Proofs of theorems that proved more or deeper results than what was first supposed or stated as the corresponding theorem - MathOverflow

big list - Every mathematician has only a few tricks - MathOverflow

Poincaré on intuition in mathematics - MacTutor History of Mathematics

There's more to mathematics than rigour and proofs | What\'s new

soft question - Is an interpretation mathematics (fit for publication)? - MathOverflow

mathematics education - Are hypergeometric series not taught often at universities nowadays, and if so, why? - MathOverflow

calculus - Is there a reason it is so rare we can solve differential equations? - Mathematics Stack Exchange

logic - How many words (i.e. not \"math\" symbols\") should I use in my proofs? - Mathematics Stack Exchange

fa.functional analysis - Why do we have two theorems when one implies the other? - MathOverflow

soft question - Theorems with many distinct proofs - MathOverflow

\"Strange\" proofs of existence theorems - MathOverflow

Studying mathematics

mathematical pedagogy - Why\'s math way more puzzling, abstruse than law and medicine? - Mathematics Educators Stack Exchange

Why there is no Hitchhiker's Guide to Mathematics for Programmers | Math ∩ Programming

mathematics - How can I counter a student response saying \"Why are we bothered to reinvent the wheel when proving mathematical identities?\" - Academia Stack Exchange

secondary education - Response to Students Who Say \"This Is Not Important\" - Mathematics Educators Stack Exchange

soft question - Daunting papers/books and how to finally read them - MathOverflow

books - Learning mathematics in an \"independent and idiosyncratic\" way - MathOverflow

Mathematical Rigour

Why is writing down mathematical proofs more fault-proof than writing computer code? - Computer Science Stack Exchange

soft question - Consequences of lack of rigour - MathOverflow

history - Soft question: Examples where lack of mathematical rigour cause security breaches? - Cryptography Stack Exchange)

Controversy in mathematics

research - Replication crisis in mathematics - MathOverflow

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

ho.history overview - Endless controversy - MathOverflow

independent researcher - Why are most cranks old men? - Academia Stack Exchange

People

Paul du Bois-Reymond - Wikipedia

James Dugundji - Wikipedia

Other

abstract algebra - Can we define algebraic structures (group, rings, modules, fields) via their arrows? - Mathematics Stack Exchange

algebra precalculus - If two pairs of numbers have equal sums and products, what can we conclude about the pairs? - Mathematics Stack Exchange

Readings | Mathematics for Computer Science | Electrical Engineering and Computer Science | MIT OpenCourseWare

Papers

Infinity - A simple, but not too simple introduction (online @ arxiv.org)

Books

The Magical Maze (borrow @ archive.org)

Archimedes' Revenge (borrow @ archive.org)

Compactness and Contradiction (online @ terrytao.wordpress.com)