Mental and physical abilities decrease with age. That is a fact of nature. The example you give is a truism. The exception proves the rule. It's great that some people can maintain their health and mental faculties much longer than the average person but in the end Father Time gets us all.
Does old age equal incompetence as a chess player?

I was a >2100 player but that was in the previous century.
What I can say :
at 45 the memory get worse, you play with less energy and you're accept more quickly a draw.
I do remember more the finesses of openings studied when I was young than those I studied last month. The short-term memory became bad.
But old people has the experience :))

Mental and physical abilities decrease with age. That is a fact of nature. The example you give is a truism. The exception proves the rule. It's great that some people can maintain their health and mental faculties much longer than the average person but in the end Father Time gets us all.
The exception tests the rule, as per the original meaning of the saying.
Likewise the proof (test) of the pudding is in the eating.

your memory became bad at 45, does not it will for everyone. I agree 90 is an exception but I think oyu can be a very good player even in your 70's

Depends on the player... Look at Sammy Reshevshy...
What I have seen with older players, is their physical stamia may faulter... Any one can make an error when they are tired...
Remember the old Mexican proverb; "The devil is not only wise because he is the devil, but he is also wise because he is very old!"

Between age [mid 40s], epilepsy & brain surgery my memory is not so sharp.
Short clocked games are not my thing.
More brains! My brain c. 2010
Absolutely not. I have lost OTB to a player who was in his 90's who still played good positional chess.

Ellie , you can improve a lot. I guess your grandchildren makes you childish (fast learning).
I am testing me, can I at the age of 52 develop as fast as the best kids in Norway . The answer is :" partially." There are two 9 year old kids in my club thas improved faster than me this autumn.
It really depends. First they have to avoid the really bad stuff, like alzheimers or dementia. Those conditions destroy all parts of a person's intellect. If you can't remember someone who visited you earlier in the day you're not going to be able to play chess very well, unless it's an extreme short term memory thing.
My dad when he got over 75 and into his 80s got slower and slower in his movements. It's almost like, everything was the same... except slower, and memory getting worse (but not ridiculous). Probably after a person is 50 they start to get measurably worse if not before. Imagine some fresh young guy full of energy, poring over the board, checking every last variation, eyes darting back and forth, memorizing and coordinating. It's not the same for older people, their calculating ability and memory is just not the same.
But they'll never lose their positional understanding and ability. They just have to be more economical with what ideas they choose to mentally test out over the board. This may sound mean but probably a good strategy against older people would be to pull them into outrageous tactics.

Is this a photo of Kortschnoi or Serper, please excuse my ignorance. He looks about my age, I would so love to meet him!

I see many Grandmaters 65 and over playing well at the International chess level. My personal opinion is that is not the age of the player, but rather their health. Some people start getting mind diseases at an early age. There are drugs available from your doctor to stop this problem (or at least slow it down). But you have to see a 'good doctor', not some old folgie who is himself having some mental problems and is not up tp date on the latest medicines.
Don
Andres Segovia was one of the most brilliant guitarists and composers of the 20th century. He was still delighting audiences in his nineties, and also at this great age he continued to run master classes. Why do people always assume the elderly are somehow deficient in intellectual ability? Your thoughts and ideas on this subject would be appreciated.