The year 1797 in science and technology involved some significant events.

• Smithson Tennant demonstrates that diamond is a pure form of carbon.^[1]
• Louis Nicolas Vauquelin discovers chromium.
• Joseph Proust proposes the law of definite proportions, which states that elements always combine in small, whole number ratios to form compounds.^[2]

• Lagrange publishes his Théorie des fonctions analytiques.

• Giovanni Battista Venturi describes the Venturi effect.^[3][4]

• October 22 – André-Jacques Garnerin carries out the first descent using a frameless parachute, a 980 m (3,200 feet) drop from a balloon in Paris.

• Thomas Bewick publishes the first volume, Land Birds, of his History of British Birds.

• Copley Medal: Not awarded^[5]

• January 3 – Frederick William Hope, British zoologist (died 1862)
• January 4 – Wilhelm Beer, Prussian astronomer (died 1850)
• February – Joseph-Alphonse Adhémar, French mathematician (died 1862)
• February 2 – Joseph Guislain, Flemish psychiatrist (died 1860)
• February 5 – Jean-Marie Duhamel, French mathematician and physicist (died 1872)
• March 10 – George Poulett Scrope, British geologist and economist (died 1876)
• March 21 – Johann Andreas Wagner, German paleontologist, zoologist and archeologist (died 1861)
• April 29 – George Don, Scottish botanist (died 1856)
• May 2 – Abraham Gesner, Canadian inventor of kerosene (died 1864)
• May 30 – Karl Friedrich Naumann, German geologist and mineralogist (died 1873)
• July 14 – James Scott Bowerbank, British naturalist, geologist and paleontologist (died 1877)
• July 26 – William Hutton, British geologist and paleontologist (died 1860)
• August 23 – Adhémar Jean Claude Barré de Saint-Venant, French mechanician and mathematician (died 1886)
• August 31 – James Ferguson, Scottish-born American astronomer (died 1867)
• September 1 – Augustin-Pierre Dubrunfaut, French chemist (died 1881)
• September 10 – Carl Gustaf Mosander, Swedish chemist (died 1858)
• September 17 – Heinrich Kuhl, German zoologist (died 1821)
• October 4 – Félix Savary, French astronomer (died 1841)
• October 5 – John Gardner Wilkinson, British egyptologist (died 1875)
• November 14 – Charles Lyell, Scottish geologist (died 1875)
• November 20 - Mary Buckland, British paleontologist and marine biologist (died 1857)
• December 3
  • Margaretta Morris, American entomologist (died 1867)
  • Andrew Smith, Scottish military surgeon, explorer, ethnologist and zoologist (died 1872)
• December 17 – Joseph Henry, American scientist (died 1878)
• December 23 – Adrien-Henri de Jussieu, French botanist (died 1853)

• March 16 – Cristina Roccati, Italian scholar in physics (born 1732)
• March 26 – James Hutton, Scottish geologist (born 1726)
• June 13 – Samuel-Auguste Tissot, Swiss physician (born 1728)
• August 29 – Joseph Wright, English painter of scientific subjects (born 1734)
• date unknown – Wang Zhenyi, Chinese Qing dynasty female astronomer and poet (born 1768)