Maximum number of moves?

Infinite, because players can repeat moves back and forth.

Not infinite, no pawn move/capture in last 50 moves causes a draw.

I retract my statement! I learned something new. I also apologize for speaking with such confidence about something I made an assumption about. I was never taught that rule.

Great question.

Edit: I think I'll stay in the beginner section of the forums for now 😂

No worries, I'm glad this caused you to learned something new about chess.

I just watched a youtube video which contains a deep explanation on the subject. It is claimed to be 5898 moves maximum possible. 

Still i need to prove it. Any contribution on calculating this is appreciated.

No, your okay. You never know what you don't know. I had forgotten the specifics of that rule myself.

Сдохни мразь, вы весь мир разрушили, мы разрушим вас ублюдки

Америка сосёт у России

Хорошего дня

Так что у России и влагалище и член одновременно? Значит Россия гермафродит ? Также почему она у мужиков. И вообще куда она ходит по ночам?

это так мило

Расскажи как нам попасть в твой мир зазеркалья где свобода это рабство, война это мир, и где незнание это сила?

(Tell us, how can we get into your world beyond the looking-glass where freedom is slavery, war is peace, and where ignorance is strength?)

I know ofno theoretical proof, but supposedly I have read somewhere before it is 5949 moves.  It does seem a little low as you can make 96 pawn moves.  6 per pawn.  To do so, capture 4 white pieces on the a, c, e, and g files with black pawns.  Capture 4 black pieces on the b, d, f, and h pawns.

So starting with 99 knight moves (through White 50), go 49 or 49 1/2 moves each time.  96 pawn moves and 30 piece captures (including the 16 promoted queens) feels like it ought to be closer to 6300, maybe 6200 and change.  So not sure where 5949 comes from.

With the 50- or -75 rules this has been calculated
https://wismuth.com/chess/longest-game.html

Even without the 50- or 75-moves rule the number is finite, but huge.
There is only a finite number of legal positions: 10^44.
https://github.com/tromp/ChessPositionRanking 
With the 3-fold or 5-fold repetition rules each of those 10^44 legal positions can only be visited 2 (or 4) times before the game ends in a draw.

Here is the longest world championship game: 136 moves
https://theweekinchess.com/chessnews/events/world-chess-championship-2021/carlsen-takes-the-lead-in-world-championship-following-a-record-breaking-game-6 

And here is the longest tournament game ever: 269 moves
https://www.chessgames.com/perl/chessgame?gid=1268705 

I have had a 134 move game over the board.

The previous world championship, Game 6, went 136.

The longest I have witnessed is 166.

thank you everyone. I'm very appreciated.