Why hasn't Russia maintained significant numbers of aircraft carriers?

This is a very interesting question. To answer it I had to see if you are correct, that indeed Russia/USSR did not have a larger number of aircraft carriers.

Based on this article, Russian Aircraft Carriers Sold Journal: American metal market, Date: 11/16/1994, Vol: 102(222): 11 - 11 you are correct. Russia did not have a large number of aircraft carriers. A South Korean company bought a decade ago two Russian aircraft carriers for scrap metal: the Minsk and Novorossiisk.

Based on the same article I have to conclude that the limited number of aircraft carriers is due to the fact that Russia believes the cold war has ended:

The two 37,000-ton aircraftcarriers, built in 1979 and 1984, were the mainstay of the Soviet Union's Far East Naval Fleet, but with the end of the Cold War, Russia decided to decommission them.

The Soviet Union believed in spreading Communism (an ideology) through giving communist revolutionaries weapons such as guns, tanks, and planes.

The USA believed in projecting military power to guard its economic interests, which included containing the spread of communism (domino theory). Sometimes the US even gave weapons to bad people (Saddam Hussein, the Taliban of Afghanistan, etc.) to counter the spread of communism or guard its economic interests. The US has good reason to believe that it cannot rely on many of its fickle "allies." Therefore the US needs another method of projecting military power. That is where the carriers come in. They are much more reliable than dictators etc. However carriers are also much more vulnerable.

Nuclear Powered Icebreakers were more important to the Soviet Union (and now Russia) because no other ships (neither aircraft carriers nor tankers) can survive the ice of the Arctic Ocean, which is where much of Russia's oil resources are located.

The Soviet Union did build aircraft carriers, but on a much more limited scale than the USA. Communism prevented the Soviet Union from trading as much as the US, since it believed in centralized economies. Centralized planning also allowed convoys of ships to have military escorts such as those to Cuba. With the end of the Cold War, Russia has little need for naval power and Ukraine (former USSR) recently sold a partially completed Soviet aircraft carrier to China.

It should also be noted that the the most humiliating defeat in America's recent history was the attack on Pearl Harbor, which was conducted from Japanese aircraft carriers.

The other answers are all correct and worth an upvote. Money, land-bound, defensive mentality were factors.

However, I will add one key element the others have not mentioned, which is that it was a deliberate part of their strategy. Soviet military planners considered the United States to be a threat to their polity and they deliberately made an "anti-USA" strategy, which dictated designing weapons and methods which were specifically for countering US technology.

In naval warfare, this meant that they deliberately decided to put all their money into submarines. The hope was that in a "sub vs carrier" war, the subs would win. By focusing completely on subs, they were hoping they could surpass us in this one key technology which would trump our other advantages.

Russia is not a true naval power. It has only a handful of ports: St. Petersburg, Vladlivostok, Archangelsk, and Sevastopol (and all but the last are icebound for several months of the year). Its naval needs are primarily defensive, meaning that it can use land-based aircraft, rather than aircraft carriers for this purpose. Of course it needs a surface fleet and submarines to defend these approaches.

The aircraft carrier is an offensive weapon; it is not very useful to protect one's own territory-- and the USSR was never planning an aggressive war. The USSR's main military preparations were for a defensive war in Europe similar to the Great Patriotic War during WWII and for nuclear deterrence so to avoid a nuclear strike from the United States.

Even in the case of war with the US, the USSR planned a land attack on the European NATO members with a massive tank rush.

The US, on the other hand, permanently conducts aggressive wars for resources against small and medium-sized countries overseas. The current military doctrine even calls for the ability to conduct two wars in two different countries at the same time.

Besides that, the best means to quickly defeat a small country is to put a carrier near its borders and to make a massive bomb strike. Transporting land weapons such as tanks on the other hand is expensive and takes much time.