Andrey Markov (Soviet mathematician) | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Andrey_....
00:00:05 Notes
00:00:08 External links
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
increases imagination and understanding
improves your listening skills
improves your own spoken accent
learn while on the move
reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services...
Other Wikipedia audio articles at:
https://www.youtube.com/results?searc...
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9904314995929699
Voice name: en-US-Wavenet-C
"I cannot teach anybody anything, I can only make them think."
Socrates
SUMMARY
=======
Andrey Andreyevich Markov Jr. (Russian: Андре́й Андре́евич Ма́рков; St. Petersburg, September 22, 1903 – Moscow, October 11, 1979) was a Soviet mathematician, the son of the Russian mathematician Andrey Andreyevich Markov Sr, and one of the key founders of the Russian school of constructive mathematics and logic. He made outstanding contributions to various areas of mathematics, including differential equations, topology, mathematical logic and the foundations of mathematics.His name is in particular associated with Markov's principle, Markov's rule, and Markov algorithm. An important result which he proved in 1947 was that the word problem for semigroups was unsolvable; Emil Post obtained the same result independently at about the same time. In 1953 he became a member of the Communist Party.
In 1960, Markov obtained fundamental results showing that the classification of four-dimensional manifolds is undecidable: no general algorithm exists for distinguishing two arbitrary manifolds with four or more dimensions. This is because four dimensional manifolds have sufficient flexibility to allow us to embed any algorithm within their structure, so that classification of all four-manifolds would imply a solution to Turing's halting problem. This result has profound implications for the limitations of mathematical analysis.