6. In this century, the 200th anniversary of the birth of the famous Russian mathematician, a native of the Kaluga province P.L. Chebyshev, will be celebrated. In the number that records his year of birth, the sum of the numbers in the hundreds and thousands place is three times the sum of the numbers in the tens and units place, and the digit in the tens place is greater than the digit in the units place. Determine the year of birth of P.L. Chebyshev, given that he was born and died in the same century and lived for 73 years.
6. Since in the 21st century the 200th anniversary of P.L. Chebyshev's birth will be celebrated, he was born in the 19th century - 18th. The sum of the numbers in the thousands and hundreds place is $9(1+8=9)$. The sum of the numbers in the tens and units place is three times less than 9. Therefore, it is $3(a+b=3)$. The number three can be represented as the sum of the following two addends: $3=0+3=1+2$. The numbers $a$ and $b$ can take the values 0 and 3 or 1 and 2. The year of birth can fall on $1803, 1830, 1812, 1821$. The numbers 1803 and 1812 should be excluded, as they do not satisfy the condition that the number of tens must be greater than the number of units. Only 1830 and 1821 remain. According to the last condition, P.L. Chebyshev lived for 73 years, was born and died in the same century. This condition is met only by the number - 1821. ( $1830+73=1903-$ this is the $\mathrm{XX}$ century).

Answer: 1821.