For 90 Years, Every Test Said This Was True | Until Mathematics Proved It Wasn't #migoroedu

Comments · 75

• MI

  @migoroedu · 12 days ago · pinned

  A conjecture can survive billions of tests and still be false.<br><br>So here’s the uncomfortable question: How much evidence would convince you that a mathematical pattern is actually true? 👇

  9

• BA

  @barakman75 · 9 days ago

  Another example worth pointing out, of an object proven to exist without being found, is of Gauss conjecture that the prime-counting function π(n) is always strictly less than the logarithmic integral li(n), which was later proven to have a counterexample at a staggering (yet unknown precisely) value.

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• NI

  @nightmisterio · 9 days ago

  I am glad you reminded me of this.

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• MA

  @MathIsNotAlwaysFun · 5 days ago

  The Mertens function can be spectrally decomposed into a superposition of oscillations associated with the zeta zeros. The oscillations have different frequencies in log x. Most of the time they partially cancel, but Diophantine approximation shows that sufficiently many important components can come into phase to force the combined signal above +1 and below -1. Because these favorable alignments recur arbitrarily far out, the Mertens bound must fail infinitely often.

  2

• KR

  @krwada · 7 days ago

  This is fantastic in many ways.<br><br>Infinity, like eternity is mind staggeringly huge.

• KU

  @kuldeepparashar7266 · 9 days ago

  Super Excellent teaching module thanks sir jee 🙏🙏💐💐

• KU

  @kuldeepparashar7266 · 9 days ago

  Super Excellent information thanks sir jee 🙏🙏💐💐

• RO

  @robsosno · 9 days ago (edited)

  There is another possibility: in the future super-power quantum computer will &nbsp;review all the numbers in the range up to 10^10^29 and will not find any case against the Martens conjecture. If this happens then it will mean that Riemann hypothesis is &nbsp;wrong.

  2

• DR

  @DrJulianNewmansChannel · 9 days ago

  It was interesting to learn more about the history of the Mertens Conjecture. And also, well done for explaining at <a href="https://www.youtube.com/watch?v=8dndLZeOKQs&amp;t=771">12:51</a>ff how there’s a connection to the Riemann Hypothesis. The following 1-minute Short states explicitly (with no advanced maths knowledge required) how the Riemann Hypothesis can be equivalently formulated as a weaker version of the Mertens Conjecture: <a href="https://www.youtube.com/shorts/qzoF0DmOae8">https://youtube.com/shorts/qzoF0DmOae8?is=_pjsXWFMVXYxSg1Y</a>

• IA

  @iamurpal2309 · 9 days ago

  his is one of the strangest things about mathematics: you can prove that a pattern must eventually fail without knowing the first place where it fails. Millions of successful tests suddenly mean very little.

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• MI

  @MirzaAli-r5c · 8 days ago

  Can you do a video on controversy of cubic equation<br><br>And cray

  1

• MA

  @markwrede8878 · 9 days ago

  Compiling from over 191 million primes, I have built a factoring machine of 150 cogs through a principle which may be applied beyond with a machine having such capacities. <a href="https://www.youtube.com/watch?v=dksj4ikvgJM&amp;t=3">https://www.youtube.com/watch?v=dksj4ikvgJM&amp;t=3s</a>