This is just an example. Riemann hypothesis. Regularity of solutions to Navier Stokes equation. P vs NP. Euler's equation of fluids. Just to name a few. Astounding open problems are all around us and the machines can do nothing about them. BOOM!
Machines have defeated us already as we are their slave!
The switches are still in our hand.
BANG ON! We built the machines and make the them do our work. Who's the slave again?
They have helped with a few. The four colour theorem was the first one to need quite a lot of computation. Some other modern proofs require a lengthy list of examples to be checked by computer. Computer proof machines have derived all of Euclid, I believe. As a mathematician, I would not belittle the possibility of computers being used as tools to do mathematics, although the power of pen and paper is still very strong!
You should solve P=NP next
No thanks, I'm too busy explaining to schmucks that .999 repeating decimal is equal to 1.
Yes, as @Elroch says, computers have helped with a few math problems, some which are quite notable. Some other examples:
1) The number [2^(74,207,281) − 1] was proven to be prime. This required hundreds of computers and many years.
2) Checkers was solved with computers. Humans helped by encoding symmetries to simplify the problem. (it still took a few years).
3) The fewest clues in a Sudoku (17) was solved with computers. Humans helped by encoding symmetries. (it still took a few years).
4) The 15th pentagon shape that can tile a plane (post #3704 in this thread) was solved with computers. This was done 30 years after the last shape was discovered, and most mathematicians didn't even know anyone was working on it, or that a new shape could even exist.
In general, the catalog of possible algorithms is bigger than the math problem itself which makes unsupported statements such as "chess will never be solved" meaningless.
I forgot the search for large primes, but it is a rather minor thing to mathematicians - not a proof of a theorem, just finding examples. The biggest primes have all been found using quite simple algorithms for checking numbers of special forms, requiring a lot of brute force for huge numbers.
The tiling discovery is a great example because it was a bit of a surprise.
Yes, as @Elroch says, computers have helped with a few math problems, some which are quite notable. Some other examples:
1) The number [2^(74,207,281) − 1] was proven to be prime. This required hundreds of computers and many years.
2) Checkers was solved with computers. Humans helped by encoding symmetries to simplify the problem. (it still took a few years).
3) The fewest clues in a Sudoku (17) was solved with computers. Humans helped by encoding symmetries. (it still took a few years).
4) The 15th pentagon shape that can tile a plane (post #3704 in this thread) was solved with computers. This was done 30 years after the last shape was discovered, and most mathematicians didn't even know anyone was working on it, or that a new shape could even exist.
In general, the catalog of possible algorithms is bigger than the math problem itself which makes unsupported statements such as "chess will never be solved" meaningless.
Thanks for shooting yourself right in the foot.
In every one of these cases, the solution was brute force calculation with added shortcuts. But, as we have already discussed many, many times...you can assume shortcuts that cut the number of chess positions to be traversed by a factor of a million (far, far, far more than was afforded in any of the cases you have listed) and still have a number that is beyond calculation using all of mankind's resources for 10s or 100s of thousands of years. Nothing you listed gives the slightest increased hope of solving chess in 10 years, 50 years, 200 years, or 50,000 years.
P.S. Your first example is misleading. The effort was/is to find more/larger prime numbers, not to find out if that specific number is prime, as you worded it 
. This kind of imprecision is exactly why you'll never really add anything to this...you don't understand most of it, and what you do understand you convey poorly.
...you can assume shortcuts..
You didn't consider every possible shortcut, nor every possible algorithm.😊
.. The complete works, {presumably, re. Anything}, of 'btickler'; Translated, into a meme.
Fair warning ; His Ego, is riding on it ! ; Therefore, the unending, 'hammering' of his adopted 'pov'.
...you can assume shortcuts..
You didn't consider every possible shortcut, nor every possible algorithm.😊
The magic argument again? I am not considering that the Universe was created specifically for penguins, either...but what I wrote applies regardless. You could tell me that you will absorb the Pacific Ocean into a handheld sponge and walk away carrying it, and I could tell you it's impossible, and your argument would be that I am just not considering all possible technological advances. That's how your argument fails.
You arguments against the word "impossible" are all based on fantasy/magic. The word impossible has never meant "completely not possible even with infinite resources and infinite time"...the word impossible means "not possible for mankind to achieve within the best understanding of the universe currently withstanding scrutiny by scientists"...and it can scarcely have any other definition. If your definition of possible is simply "able to be conceived", then there's no need for the distinction of the word "impossible" at all. There would be no circles overlapping in your little Venn diagrams, it would all be one circle of magic wish fulfillment. All things = possible. No need for the words possible or impossible using that equation. Yet, we have the words. Impossible means something.
If you can grok this simple concept, you will reach a higher plane of logic than your past postings have indicated you are capable of ...
This is usually where you break out your Copernicus argument...which is also fallacious. Just because someone can discover something heretofore unknown does not mean you can state that all things conceivable will be discovered to be true eventually. The "nobody believed Copernicus either" argument discounts the hundreds of thousands of hairbrained suppositions that turned out not to be true or possible:
- Altruitus said that the earth revolves around a can of tuna that had not been invented yet. He was boiled in olive oil.
- Gullibedes said that the the earth was a potato and that the heavenly bodies were 2 dimensional french fries cooked in a space filled with olive oil. They threw him off a tower because boiling him in oil would have implied he was heavenly...
Etc.
.. The complete works, {presumably, re. Anything}, of 'btickler'; Translated, into a meme.
Fair warning ; His Ego, is riding on it ! ; Therefore, the unending, 'hammering' of his adopted 'pov'.
Stick to OCD punctuation. Meme posting is what millenials that can't argue their way out of a paper bag resort to. You might as well wear a sign that says "I can't think for myself and I find one line concepts to be very relatable! Also, I like pictures.".
The magic argument again? I am not considering that the Universe was created specifically for penguins, either...but what I wrote applies regardless. You could tell me that you will absorb the Pacific Ocean into a handheld sponge and walk away carrying it, and I could tell you it's impossible, and your argument would be that I am just not considering all possible technological advances. That's how your argument fails.
You arguments against the word "impossible" are all based on fantasy/magic. The word impossible has never meant "completely not possible even with infinite resources and infinite time"...the word impossible means "not possible for mankind to achieve within the best understanding of the universe currently withstanding scrutiny by scientists"...and it can scarcely have any other definition. If your definition of possible is simply "able to be conceived", then there's no need for the distinction of the word "impossible" at all. There would be no circles overlapping in your little Venn diagrams, it would all be one circle of magic wish fulfillment. All things = possible. No need for the words possible or impossible using that equation. Yet, we have the words. Impossible means something.
If you can grok this simple concept, you will reach a higher plane of logic than your past postings have indicated you are capable of ...
This is usually where you break out your Copernicus argument...which is also fallacious. Just because someone can discover something heretofore unknown does not mean you can state that all things conceivable will be discovered to be true eventually. The "nobody believed Copernicus either" argument discounts the hundreds of thousands of hairbrained suppositions that turned out not to be true or possible:
- Altruitus said that the earth revolves around a can of tuna that had not been invented yet. He was boiled in olive oil.
- Gullibedes said that the the earth was a potato and that the heavenly bodies were 2 dimensional french fries cooked in a space filled with olive oil. They threw him off a tower because boiling him in oil would have implied he was heavenly...
Etc. Stick to OCD punctuation. Meme posting is what millenials that can't argue their way out of a paper bag resort to. You might as well wear a sign that says "I can't think for myself and I find one line concepts to be very relatable! Also, I like pictures.".
A lot of text but nothing said.🤡
A lot of text but nothing said.🤡
Nothing you understood, perhaps.
Actually nothing.😊
Actually nothing.😊
It's fine if you feel that way...I feel the same about your postings. Nevertheless, what I said makes short work of your fuzzy logic (which is why you never respond my direct points), and will continue to do so. Enjoy.
You've rarely made a direct point to the topic of this thread.😛
You've rarely made a direct point to the topic of this thread.😛
Well, that's because you have a short memory.
I made most of my unrefuted direct points back around pages 60-80. I rarely repeat direct points and if I do, I mention that I have made the same point before...even then I usually state it some new way so that it might be understood. It's not my fault you can never understand anything past an 8th grade level . You, on the other hand, post the same tired diagrams over and over. They are as fluffy as meaningless each time.
My goal here is not to convince you, really, you're a lost cause...it's just to remind other readers that this thread is full of misinformation and badly thought out theories. This helps prevent said crap from proliferating to other threads.
https://www.yahoo.com/news/mathematicians-awarded-3-million-cracking-170200711.html