Elon Musk, the world's richest person, now has a major influence on Twitter's (TWTR) operations and many are wondering what he has in store.

On Tuesday, Musk gained a 9% stake in Twitter and a seat on its corporate board. He immediately took to the social media site to share his thoughts about the direction of a publicly traded company worth about $40.5 billion.

“Looking forward to working with Parag [Agrawal] & Twitter board to make significant improvements to Twitter in coming months,” Musk said on Twitter Tuesday.

Some believe that Musk's addition to the board will boost transparency since he has described himself as a “free speech absolutist.” But others believe that it could take an “irresponsible” spin.

There is greater hope from investors that Musk can influence the company's value. Shares of Twitter would jump 33.6% after the disclosure of Musk's stake, boosting his fortune by about $1.2 billion.

"It's nice when a company reports profits — it seems much better if a company reports its association with Elon Musk," Howard Fischer, a partner at the law firm Moses & Singer in New York and a former lawyer at the Securities and Exchange Commission, told CNBC.

"[Musk] may not improve operations, he may not improve revenue, he may not lower liabilities, but the stock market rewards [Twitter]," Fischer added.

Musk is a frequent user of Twitter, making him familiar with changes that many would like to see happen. He has hinted at making Twitter's algorithm viewable by the public, widening the availability of "verified" Twitter accounts, and NFT profile pictures. He also has a strong proponent of cryptocurrency and Musk has suggested that Dogecoin could be used to pay for Twitter Blue, a subscription service that allows for exclusive access to special Twitter features.

Seeking a minor tweak to tweets, Musk had asked his Twitter followers on Monday if they would prefer an “edit button.”

It remains unclear what the ultimate goal is for Musk, who is known for eccentric business decisions. His presence could mean many directions for the social media site.

"Maybe Elon Musk secretly wants to blow (Twitter) up ... maybe he wants to destroy it," Syracuse University communications professor Jennifer Grygiel told the Washington Post.

Wedbush analyst Dan Ives doesn't expect Musk to be a silent contributor.

"This is just the appetizer," Ives told Yahoo Finance. "Ultimately, we believe he will have an active stake over the coming weeks or month. This is just a start. I think he will have a broader strategic focus on Twitter, whether it's changing the slate, changing the management team or ultimately a buyout."