MathOverflow

Key takeaways

MathOverflow belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect MathOverflow to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of MathOverflow from memory before moving on to harder problems.

Reference excerpt

MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. It is a part of the Stack Exchange Network, but distinct from math.stackexchange.com. It is primarily for asking questions on mathematics research – i.e. related to unsolved problems and the extension of knowledge of mathematics into areas that are not yet known – and does not welcome requests from non-mathematicians for instruction, for example homework exercises. It does welcome various questions on other topics that might normally be discussed among mathematicians, for example about publishing, refereeing, advising, getting tenure, etc. It is generally inhospitable to questions perceived as tendentious or argumentative.

Origin and history The website was started by Berkeley graduate students and postdocs Anton Geraschenko, David Zureick-Brown, and Kim Morrison on 28 September 2009 based on the idea of Sándor Kovács's NSF CAREER Grant. The hosting was supported by Ravi Vakil. The site originally ran on a separate installation of the StackExchange 1.0 software engine; on June 25, 2013, it was integrated in the regular Stack Exchange Network, running SE 2.0.

Naming According to MathOverflow FAQ, the proper spelling is "MathOverflow" rather than "Math Overflow".

Use of mathematical formulas The original version of the website did not support LaTeX markup for mathematical formulas. To support most of the functionality of LaTeX, MathJax was added in order for the site to transform math equations into their appropriate forms. In its current state, any post including "Math Mode" (text between $s) will translate into proper mathematical notation.

Usage As of April 4, 2012, there were 16,496 registered users on MathOverflow, most of whom were located in the United States (35%), India (12%), and the United Kingdom (6%). By December 11, 2018, the number of registered users had grown to 87,850. As of June 2019, 123,448 questions have been posted. In 2011, questions were answered an average of 3.9 hours after they were posted, and "Acceptable" answers took an average of 5.01 hours.

Reception Terence Tao compared it to "the venerable newsgroup sci.math, but with more modern, 'Web 2.0' features". John C. Baez writes that "website 'Math Overflow' has become a universal clearinghouse for math questions". According to Gil Kalai, MathOverflow "is ran [sic] by an energetic and impressive group of very (very very) young people". Jordan Ellenberg comments that the website "offers a constantly changing array of new questions" and is "addictive" in a "particularly pure form", as he compares it to the Polymath Project. Jared Keller in The Atlantic writes: "Math Overflow is almost an anti-social network, focused solely on productively addressing the problems posed by its users." He quotes Kim Morrison saying: "Mathematicians as a whole are surprisingly skeptical of many aspects of the modern Internet... In particular, things like Facebook, Twitter, etc. are viewed as enormous wastes of time."

See also List of mathematical software nLab PhysicsOverflow Project Euler — computational mathematics and computer programming problem solving website

Notes

Further reading Tausczik, Yla R.; Kittur, Aniket; Kraut, Robert E. (2014). "Collaborative Problem Solving: A Study of MathOverflow". Proceedings of the 17th ACM Conference on Computer Supported Cooperative Work & Social Computing (CSCW '14), Baltimore, Maryland, USA. New York, NY, USA: ACM. pp. 355–367. doi:10.1145/2531602.2531690. ISBN 978-1-4503-2540-0. Montoya, Leydi Viviana; Ma, Athen; Mondragón, Raúl J. (2013). "Social Achievement and Centrality in MathOverflow". In Ghoshal, Gourab; Poncela-Casasnovas, Julia; Tolksdorf, Robert (eds.). Complex Networks IV: Proceedings of the 4th Workshop on Complex Networks (CompleNet 2013). Berlin and Heidelberg: Springer. pp. 27–38. doi:10.1007/978-3-642-36844-8_3. Martin, Ursula; Pease, Alison (2013). "Mathematical Practice, Crowdsourcing, and Social Machines". In Carette, Jacques; Aspinall, David; Lange, Christoph; Sojka, Petr; Windsteiger, Wolfgang (eds.). Intelligent Computer Mathematics: MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of the International Conference on Intelligent Computer Mathematics (CICM 2013), Bath, UK, July 8-12, 2013, Proceedings. Lecture Notes in Computer Science. Vol. 7961. Berlin and Heidelberg: Springer. pp. 98–119. arXiv:1305.0900. doi:10.1007/978-3-642-39320-4_7.

External links Official website "Podcast #86". Stack Exchange Blog. 23 March 2010. — podcast with Joel Spolsky and Jeff Atwood (creators of Stack Exchange) and Anton Geraschenko (creator of MathOverflow).

Worked examples

Example 1 — a first encounter with MathOverflow

Start with the simplest possible case. Write down what MathOverflow claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to MathOverflow before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about MathOverflow ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of MathOverflow

In research: MathOverflow appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses MathOverflow in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: MathOverflow is common in secondary-school and first-year university syllabi. It links to neighbouring topics Internet properties established in 2009, Mathematics websites, Stack Exchange network, so understanding it makes those chapters shorter.
In everyday life: Look for MathOverflow outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study MathOverflow in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MathOverflow means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain MathOverflow out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MathOverflow in simple terms?

MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities.

Why does MathOverflow matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study MathOverflow?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on MathOverflow.