To replace an aging battleship, a new super battleship (the future Yamato) is proposed to the Navy. Admirals Yamamoto and Nagano believe that battleships are becoming obsolete, and advocate building a new aircraft carrier instead, but they are opposed by the Navy's old guard.

Yamamoto and Nagano enlist Tadashi Kai, an eccentric, headstrong, and pacifist mathematics prodigy on the autism spectrum with an obsession for measuring things. Kai is at first unwilling to help Yamamoto and Nagano, but becomes convinced that a super battleship will be seen by other nations as an aggressive threat, leading Japan and the world toward war, and agrees to work for them.

Much of the film revolves around Kai's efforts to prove that the cost of the Yamato will be much higher than its designers claim. This he finally does, using mathematical formulas that, in a dramatic scene, are shown to be very accurate when applied to the cost of earlier ships. Kai thus demonstrates that the battleship will cost about double the estimate. But battleship champion Shigetarō Shimada, when caught in his lie, appeals to patriotism: he had deliberately underestimated the cost of the battleship so that it would be approved, as he believed it to be vitally necessary for the Navy. Shimada's scheme was to underpay the shipyard for the cost of the battleship, making up the difference by overpaying for some cruisers. Despite the exposed fraud, the proposal to the build the Yamato is approved.^[2][3][4][5]

• Masaki Suda as Lt. Commander / Commander Tadashi Kai^[6]
• Hiroshi Tachi as Rear Admiral / Admiral Isoroku Yamamoto
• Tasuku Emoto as Ensign Shōjirō Tanaka
• Minami Hamabe as Kyōko Ozaki
• Min Tanaka as Vice Admiral Tadamichi Hirayama
• Jun Kunimura as Vice Admiral Osami Nagano
• Isao Hashizume as Rear Admiral Shigetarō Shimada
• Eita Okuno as Sub-lieutenant Kunihiko Takato
• Katsuya Kobayashi as Admiral Mineo Ōsumi
• Hajime Yamazaki as Rear Admiral Yoshio Fujioka
• Fumiyo Kohinata as Captain Sekizō Uno
• Shōfukutei Tsurube as Kiyoshi Ōsato
• Kenichi Yajima as Tomekichi Ozaki

In July 2018, Yamazaki announced the production will start and entitled The Great War of Archimedes based on a manga by Norifusa Mita, this picture about the building of the battleship Yamato, and starred Masaki Suda in his first collaboration with Yamazaki.^[7] Voice actors for the dubbing into English include Luis Bermudez, Brent Mukai, Lizzy Laurenti, and Dylan Mobley.^{[citation needed]}

At the 2020 Japanese Academy Awards, Tasuku Emoto was nominated in the Best Supporting Actor category, and Masaki Suda was nominated in the Best Actor category, for their work in this film.^[6]

• The Great War of Archimedes at IMDb