Formal Methods in Mathematics

In January 2020, I attended Formal Methods in Mathematics / Lean Together 2020

Formal Mathematics, broadly, is the process of documenting mathematics including but not limited to definitions, theorems, proofs, algorithms in a manner that their correctness can be verified by a computer. One of the primary purpose of doing this is to gain confidence in the correctness of proofs. We also believe that in the near future formal mathematics would help mathematicians use computers in their quest for finding proofs.

This is a topic I have been interested for a while now. Ask me anything!

3 months, 4 weeks ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

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Can you show an example of how it is done?

- 3 months, 2 weeks ago

It looks like this. In the linked tutorial, they prove some basic properties about real numbers.

You can also try out this game which teaches some of the features of this system step-by-step.

Does this help?

- 3 months, 1 week ago

The game was certainly fun.

- 3 months, 1 week ago

I am glad you think so. If you enjoy this, there are various other things you can do: including proving some of these for fun, or contributing to the lean mathlib

- 3 months, 1 week ago

Would certainly check them out, thanks!

- 3 months, 1 week ago

- 3 months ago

Check out this link. Looks like they have updated some things.

- 2 months, 3 weeks ago

Sounds nice

- 2 months, 4 weeks ago

Yes! Proof Assistants convert the process of writing mathematical proofs into a computer game, in a way. I'd be happy to talk more about this in the comments if you are interested.

- 2 months, 3 weeks ago