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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

8 votes

What is the oldest open math problem outside of number theory?

The inverse Galois problem is another possible candidate, though it may not be easy to track down the earliest explicit statement of it. Wikipedia claims that it was posed in the early 19th century, b …
Timothy Chow's user avatar
  • 82.7k
15 votes

What is the oldest open math problem outside of number theory?

I suggested this candidate in a comment: For which $d$ and $g$ does there exist a curve in $\mathbb{P}^3$ of degree $d$ and genus $g$? In Hartshorne's Algebraic Geometry, Chapter VI, Section 6, it is …
Timothy Chow's user avatar
  • 82.7k
12 votes

What is the oldest open math problem outside of number theory?

The Navier–Stokes equation was mentioned in a comment so I thought I would give a link to Sylvio R. Bistafa's essay, 200 Years of the Navier-Stokes Equation, which gives some historical information. B …
Timothy Chow's user avatar
  • 82.7k
7 votes

Analogues of P vs. NP in the history of mathematics

A couple of other answers have mentioned Shelah and cardinal invariants, but not the following famous result that IMO is a pretty good answer to Scott's question. Theorem (Malliaris–Shelah). $\mathfr …
C7X's user avatar
  • 2,031
45 votes

Endless controversy about the correctness of significant papers

Stanley Yao Xiao's comment has been upvoted so highly that it seems worth posting as an answer. There is a currently unresolved controversy over Shinichi Mochizuki's claimed proof of the abc conjectur …
Timothy Chow's user avatar
  • 82.7k
7 votes

What's the earliest result (outside of logic) that cannot be proven constructively?

A somewhat different type of example, not as early as the ones in Andrej Bauer's answer, but perhaps a bit more resistant to "moving the goalposts," is an ineffective result in number theory. For exam …
Timothy Chow's user avatar
  • 82.7k
2 votes

What do named "tricks" share?

A trick is a mathematical life hack. A life hack is a simple but unexpected solution to a somewhat frequently occurring problem. So it is with a trick; it provides a simple and unexpected solution to …
Timothy Chow's user avatar
  • 82.7k
9 votes

When has the scaffolding been more important than the completed building?

I see several different ways of interpreting the question. The comic seems to be talking about mistakes (false starts, blind alleys, etc.) made along the way to a mathematical discovery. I think that …
José Hdz. Stgo.'s user avatar
1 vote

What are examples of mathematical concepts named after the wrong people? (Stigler's law)

De Bruijn sequences are so named because Nicolaas Govert de Bruijn enumerated them in 1946, but he later acknowledged the priority of C. Flye Sainte-Marie, who enumerated them already in 1894.
Timothy Chow's user avatar
  • 82.7k
15 votes

Examples of bad notation and its consequences

Suppose that $A$ is an oracle; then it is standard to write $\mathsf{P}^A$ for the complexity class $\mathsf{P}$ relativized to $A$. As I have mentioned elsewhere on MO, this is incredibly confusing …
Timothy Chow's user avatar
  • 82.7k
13 votes

What is an important mathematical question?

I want to point out that you raised two questions, and in my opinion they are very different questions. So I really want to know how to decide whether a question is worth studying? How do I deci …
Timothy Chow's user avatar
  • 82.7k
16 votes

Comparative analysis of history of mathematics

I'm not aware of anything exactly like what you have in mind, but here are a few things which might be close. They all take aim at the widespread belief that the intellectual development of mathemati …
Timothy Chow's user avatar
  • 82.7k
11 votes

The name for an assumption made for the sake of contradiction

Especially in the philosophy of religion, the term reductio premise is sometimes used. A Google Scholar search for "reductio premise" (in quotation marks) turns up a few dozen references; one of the …
Timothy Chow's user avatar
  • 82.7k
1 vote

Fiction books about mathematicians?

After Math by Miriam Webster is a kind of mystery novel set in a department of mathematics. The main characters are mathematicians and there is a considerable amount of mathematics in the book; I bel …
Martin Sleziak's user avatar
3 votes

Extremely messy proofs

Given a homogeneous polynomial ideal, we can ask how many linearly independent homogeneous polynomials of each degree there are, and thereby obtain a sequence of integers. In a 1927 paper, Macaulay a …
Martin Sleziak's user avatar

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