Mathematics ----------- [(Up)](../../README.md#topics) | _See also: [FoM](../FoM/README.md#fom), [Probability Theory](../Probability%20Theory/README.md#probability-theory), [Combinatorics](../Combinatorics/README.md#combinatorics), [Group Theory](../Group%20Theory/README.md#group-theory), [Order Theory](../Order%20Theory/README.md#order-theory), [Category Theory](../Category%20Theory/README.md#category-theory), [Closure Systems](../Closure%20Systems/README.md#closure-systems), [Topology](../Topology/README.md#topology), [Matroid Theory](../Matroid%20Theory/README.md#matroid-theory), [Numerical Analysis](../Numerical%20Analysis/README.md#numerical-analysis), [Recreational Mathematics](../Recreational%20Mathematics/README.md#recreational-mathematics)_ - - - - ### Web resources ### Practice of mathematics [Examples of common false beliefs in mathematics. - MathOverflow](http://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics) ★ [soft question - Math papers where the only issue is that someone else could\'ve done it but didn\'t - MathOverflow](https://mathoverflow.net/questions/433686/math-papers-where-the-only-issue-is-that-someone-else-couldve-done-it-but-didn) ★ [soft question - When has the scaffolding been more important than the completed building? - MathOverflow](https://mathoverflow.net/questions/459252/when-has-the-scaffolding-been-more-important-than-the-completed-building) ★ [soft question - Big ideas that began small or small ideas that became big - MathOverflow](https://mathoverflow.net/questions/369179/big-ideas-that-began-small-or-small-ideas-that-became-big) ★ [reference request - Proofs of theorems that proved more or deeper results than what was first supposed or stated as the corresponding theorem - MathOverflow](https://mathoverflow.net/questions/385732/proofs-of-theorems-that-proved-more-or-deeper-results-than-what-was-first-suppos) ★ [big list - Every mathematician has only a few tricks - MathOverflow](https://mathoverflow.net/questions/363119/every-mathematician-has-only-a-few-tricks) ★ [Poincaré on intuition in mathematics - MacTutor History of Mathematics](https://mathshistory.st-andrews.ac.uk/Extras/Poincare_Intuition/) 🏛️ [There's more to mathematics than rigour and proofs \| What\'s new](https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/) ★ [soft question - Is an interpretation mathematics (fit for publication)? - MathOverflow](https://mathoverflow.net/questions/386789/is-an-interpretation-mathematics-fit-for-publication) ★ [mathematics education - Are hypergeometric series not taught often at universities nowadays, and if so, why? - MathOverflow](https://mathoverflow.net/questions/391124/are-hypergeometric-series-not-taught-often-at-universities-nowadays-and-if-so) ★ [calculus - Is there a reason it is so rare we can solve differential equations? - Mathematics Stack Exchange](https://math.stackexchange.com/questions/3782499/is-there-a-reason-it-is-so-rare-we-can-solve-differential-equations) ★ [logic - How many words (i.e. not \"math\" symbols\") should I use in my proofs? - Mathematics Stack Exchange](https://math.stackexchange.com/questions/2701182/how-many-words-i-e-not-math-symbols-should-i-use-in-my-proofs) ★ [fa.functional analysis - Why do we have two theorems when one implies the other? - MathOverflow](https://mathoverflow.net/questions/397286/why-do-we-have-two-theorems-when-one-implies-the-other) ★ [soft question - Theorems with many distinct proofs - MathOverflow](https://mathoverflow.net/questions/401493/theorems-with-many-distinct-proofs/401519) ★ [\"Strange\" proofs of existence theorems - MathOverflow](https://mathoverflow.net/questions/312439/strange-proofs-of-existence-theorems) ★ ### Studying mathematics [mathematical pedagogy - Why\'s math way more puzzling, abstruse than law and medicine? - Mathematics Educators Stack Exchange](https://matheducators.stackexchange.com/questions/24706/whys-math-way-more-puzzling-abstruse-than-law-and-medicine) ★ [Why there is no Hitchhiker's Guide to Mathematics for Programmers \| Math ∩ Programming](http://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/#comment-1345) ★ [mathematics - How can I counter a student response saying \"Why are we bothered to reinvent the wheel when proving mathematical identities?\" - Academia Stack Exchange](https://academia.stackexchange.com/questions/155433/how-can-i-counter-a-student-response-saying-why-are-we-bothered-to-reinvent-the) ★ [secondary education - Response to Students Who Say \"This Is Not Important\" - Mathematics Educators Stack Exchange](https://matheducators.stackexchange.com/questions/20962/response-to-students-who-say-this-is-not-important) ★ [soft question - Daunting papers/books and how to finally read them - MathOverflow](https://mathoverflow.net/questions/463287/daunting-papers-books-and-how-to-finally-read-them) ★ [books - Learning mathematics in an \"independent and idiosyncratic\" way - MathOverflow](https://mathoverflow.net/questions/371038/learning-mathematics-in-an-independent-and-idiosyncratic-way) ★ ### Mathematical Rigour [Why is writing down mathematical proofs more fault-proof than writing computer code? - Computer Science Stack Exchange](https://cs.stackexchange.com/questions/85327/why-is-writing-down-mathematical-proofs-more-fault-proof-than-writing-computer-c) ★ [soft question - Consequences of lack of rigour - MathOverflow](https://mathoverflow.net/questions/324257/consequences-of-lack-of-rigour) ★ [history - Soft question: Examples where lack of mathematical rigour cause security breaches? - Cryptography Stack Exchange](https://crypto.stackexchange.com/questions/71024/soft-question-examples-where-lack-of-mathematical-rigour-cause-security-breache)) ★ ### Controversy in mathematics [research - Replication crisis in mathematics - MathOverflow](https://mathoverflow.net/questions/370898/replication-crisis-in-mathematics) ★ [Titans of Mathematics Clash Over Epic Proof of ABC Conjecture \| Quanta Magazine](https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/) ★ [The ABC conjecture has (still) not been proved \| Persiflage](https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/) ★ [Notes on the Oxford IUT workshop by Brian Conrad \| mathbabe](https://mathbabe.org/2015/12/15/notes-on-the-oxford-iut-workshop-by-brian-conrad/) ★ [ho.history overview - Endless controversy - MathOverflow](https://mathoverflow.net/questions/282742/endless-controversy) ★ [independent researcher - Why are most cranks old men? - Academia Stack Exchange](https://academia.stackexchange.com/questions/145242/why-are-most-cranks-old-men) ★ ### People [Paul du Bois-Reymond - Wikipedia](https://en.wikipedia.org/wiki/Paul_du_Bois-Reymond) [James Dugundji - Wikipedia](https://en.wikipedia.org/wiki/James_Dugundji) ### Other [abstract algebra - Can we define algebraic structures (group, rings, modules, fields) via their arrows? - Mathematics Stack Exchange](https://math.stackexchange.com/questions/3586965/can-we-define-algebraic-structures-group-rings-modules-fields-via-their-arr#3588120) ★ [algebra precalculus - If two pairs of numbers have equal sums and products, what can we conclude about the pairs? - Mathematics Stack Exchange](https://math.stackexchange.com/questions/4825276/if-two-pairs-of-numbers-have-equal-sums-and-products-what-can-we-conclude-about) ★ [Readings | Mathematics for Computer Science | Electrical Engineering and Computer Science | MIT OpenCourseWare](https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/pages/readings/) ★★ _(in [Type Systems](../Type%20Systems/README.md#type-systems))_ [The algebra (and calculus!) of algebraic data types](https://codewords.recurse.com/issues/three/algebra-and-calculus-of-algebraic-data-types) ★★★ ### Papers Infinity - A simple, but not too simple introduction (online @ [arxiv.org](https://arxiv.org/abs/1506.06319)) ★★★ [💭](commentary/Chris%20Pressey.md#infinity---a-simple-but-not-too-simple-introduction) ### Books The Magical Maze (borrow @ [archive.org](https://archive.org/details/magicalmazeseein0000stew)) ★★★ Archimedes' Revenge (borrow @ [archive.org](https://archive.org/details/archimedesreveng00hoff_0)) ★ Compactness and Contradiction (online @ [terrytao.wordpress.com](https://terrytao.wordpress.com/wp-content/uploads/2011/06/blog-book.pdf))