# Linked Questions

14 questions linked to/from Widely accepted mathematical results that were later shown to be wrong?

**11**

votes

**2**answers

992 views

### What is the longest recorded gap between “proof” of a “theorem” and discovery that the result is false [duplicate]

I hope this question is not a duplicate. I am motivated by wondering when widely accepted results may be considered have a secure place in the mathematical literature. The question is intended to ...

**179**

votes

**42**answers

67k views

### Most interesting mathematics mistake?

Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove ...

**70**

votes

**36**answers

15k views

### What are some correct results discovered with incorrect (or no) proofs?

Many famous results were discovered through non-rigorous proofs, with
correct proofs being found only later and with greater difficulty. One that is well
known is Euler's 1737 proof that
$1+\frac{1}{...

**40**

votes

**25**answers

7k views

### Examples of conjectures that were widely believed to be true but later proved false

It seems to me that almost all conjectures (hypotheses) that were widely believed by mathematicians to be true were proved true later, if they ever got proved. Are there any notable exceptions?

**120**

votes

**6**answers

14k views

### what mistakes did the Italian algebraic geometers actually make?

It's "well-known" that the 19th century Italian school of algebraic geometry made great progress but also started to flounder due to lack of rigour, possibly in part due to the fact that foundations (...

**61**

votes

**7**answers

8k views

### Theorems demoted back to conjectures

Many mathematicians know the Four Color Theorem and its history: there were two alleged proofs in 1879 and 1880 both of which stood unchallenged for 11 years before flaws were discovered.
I am ...

**45**

votes

**5**answers

6k views

### Have the tides ever turned twice on any open problem?

Oftentimes open problems will have some evidence which leads to a prevailing opinion that a certain proposition, $P$, is true. However, more evidence is discovered, which might lead to a consensus ...

**35**

votes

**6**answers

3k views

### Negative impact of wrong or non-rigorous proofs

The recent talks of Voevodsky (for example, http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf), which describe subtle errors in proofs by him as well as others, as well ...

**31**

votes

**2**answers

7k views

### The error in Petrovski and Landis' proof of the 16th Hilbert problem

What was the main error in the proof of the second part of the 16th Hilbert problem by Petrovski and Landis?
Please see this related post and also the following post.. For Mathematical ...

**19**

votes

**3**answers

1k views

### Did Cauchy think that uniform and pointwise convergence were equivalent?

I've heard that Cauchy thought he'd proved that pointwise and uniform convergence are equivalent. Is this a historical fact? If it is indeed true, I was wondering if anyone had a reference.

**15**

votes

**3**answers

1k views

### Proof correctness problem

I was watching this talk by Vladimir Voevodsky which was given at the Institute of Advanced Study in 2006.
In his talk the first slide he shows has the following written on it:
...

**11**

votes

**2**answers

1k views

### Is the Steiner ratio Gilbert–Pollak conjecture still open?

Gilbert-Pollak conjecture on the Steiner ratio: Consider a set $P$ of $n$ points on the euclidean plane. A shortest
network interconnecting $P$ must be a tree, which is called a Steiner minimum ...

**6**

votes

**1**answer

599 views

### Are there 'finitistic' nonrecursive functions (assuming Church's Thesis is false)?

[Note: In what follows, I will be using the same type of argument Laszlo Kalmar did in his paper "An Argument Against the Plausibility of Church's Thesis" found in Constructivity in Mathematics, (...

**15**

votes

**2**answers

1k views

### Most papers ever “recalled” due to a flawed result?

Prompted by this bit of news,
http://www.wired.co.uk/article/fmri-bug-brain-scans-results
where a bug in MRI software has the potential to nullify up to 40,000 published papers. Has anything analogous ...