Having secured the men's 1,500m on the opening day of action, Szymanski won the 1,000m and the 5,000 to make it three golds in two days.
Szymanski edged Even Johansen by just 0.01 seconds to take the title, with another Norwegian Espen Tveit claiming bronze.
"I was hoping for a medal position, but 1,000m is not my favourite distance," Szymanski said. "Weather conditions were a little bit difficult, and the ice did not have such a glide as before. For me that was better and I won.
World University Championships
Poland finish on high
04/01/2013 AT 01:29
"I have never had such a good start in the 1,000m," he added.
Szymanski made it two wins for the day in the 5,000m, beating Norway's Martin Bjertnes to gold, with Czech Zdenek Haselberger taking bronze.
In the women's section, another Czech Martina Sablikova won her battle with two Polish skaters in the 1,500m to claim her second gold of the championships.
Sablikova sped to victory over Natalia Czerwonka and Katarzyna Wozniak.
"I think that my race was technically good," silver medallist Czerwonka said. "I lost only one second to Martina.
"Of course I am dreaming of beating her. But I am really happy with the second place."
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04/01/2013 AT 01:26
World University Championships
Szymanski gives Poland encouraging start in Zakopane
04/01/2013 AT 01:21