Other than Russel's paradox, are there other important paradoxes that shaped the history of mathematics?

## 3 Answers

Banach Tarski Paradox
Zeno's paradox. Make ancient Greek suspicious of infinity.

Liar's paradox, Quine's paradox, etc. many related paradox leads to various results in logic, such as Godel's incompleteness.

Grandi's series paradox. Part of the reason why calculus is made formally rigorous.
Zeno's paradoxes were part of the reason the Greeks were so conflicted about anything involving infinities or measurements.

The Banach-Tarski paradox is a great example of why Axiom of Choice is controversial. You can essentially make two spheres out of just one sphere that are all the same size.

Not sure if there's a name for it since it's not really a paradox, but for a century, mathematicians couldn't easily explain why the definition of a derivative didn't involve dividing by 0. People knew that their current understanding of it seemed to involve dividing by 0, but they also knew calculus was right since we could apply to physics. It led to the development of analysis, which later provided more precise definitions for things like limits and derivatives that don't involve any division by 0.

## Related questions

0 like 0 dislike
1 answer
Are the S3/S4 Edexcel Further Maths units useful to become an actuary? Topics include sampling, unbiased and biased estimators, confidence intervals and significance test...
0 like 0 dislike
20 answers
Considering leaving the actuarial profession. What are some interesting fields you've heard of former actuaries going into? How did they get into the new field?
0 like 0 dislike
9 answers
Has anyone successfully guessed on like half of the questions on an exam and still passed?
0 like 0 dislike
2 answers
The Actuarial Education Company finally removed the dictionary definition of "final solution" from their binders
0 like 0 dislike
2 answers
I did this all wrong but got the right answer? Took half of .075, used d=(1+i)/i to get discount rate, and just added. Decimal was off, but i got the numbers right. Luck?...