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Joined 1 year ago
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Cake day: June 18th, 2023

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  • As you said, we have infinite numbers so the fact that something works till 4x10^18 doesn’t prove that it will work for all numbers. It will take only one counterexample to disprove this conjecture, even if it is found at 10^100. Because then we wouldn’t be able to say that “all” even numbers > 2 are a sum of 2 prime numbers.

    So mathematicians strive for general proofs. You start with something like: Let n be any even number > 2. Now using the known axioms of mathematics, you need to prove that for every n, there always exists two prime numbers p,q such that n=p+q.

    Would recommend watching the following short and simple video on the Pythagoras theorem, it’d make it perfectly clear how proofs work in mathematics. You know the theorem right? For any right angled triangle, the square of the hypotenuse is equal to the sum of squares of both the sides. Now we can verify this for billions of different right angled triangles but it wouldn’t make it a theorem. It is a theorem because we have proved it mathematically for the general case using other known axioms of mathematics.

    https://youtu.be/YompsDlEdtc



  • I know there’s a lot of hate on the crypto stuff that Brave pushes in their browser. Heck I don’t use their browser because of it (and also because I don’t support Chromium). But I’ve been using Brave search as the default on Firefox since a few months now and it is honestly pretty good. Much better than Google and Bing/DDG most of the time (for the other times, I do switch to Google). I really really like their AI summarizer and the discussions tab. With them now serving images as well, Brave search is feature-complete as far as I’m concerned. Just happy to see a real competitor to the big tech search, not even leeching off of their index like most others do.