The phrase implies praising oneself, usually excessively and not appreciated by others. He's good at math, but he shouldn't blow his own trumpet every chance he gets.
Pro Tip 2/3
Informal Context
Used in casual conversations among friends or colleagues, but not in formal settings. At the reunion, Jim was blowing his own trumpet about his new business venture.
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Perceived Negativity
Often viewed negatively, as it can seem arrogant or lacking humility. Even though Lisa volunteered successfully, people were turned off by her blowing her own trumpet.