(Thanks to Yeshu Kolodny) We now know that the age of the earth is 4.54±1% Billion years.
From Wikipedea: In 1862, the physicist William Thomson (who later became Lord Kelvin) of Glasgow published calculations that fixed the age of Earth at between 20 million and 400 million years. He assumed that Earth had formed as a completely molten object, and determined the amount of time it would take for the near-surface to cool to its present temperature. His calculations did not account for heat produced via radioactive decay (a process then unknown to science) or convection inside the Earth, which allows more heat to escape from the interior to warm rocks near the surface.
Test your intuition/knowledge
What was the main reason for Lord Kelvin’s wrong estimation
a) Radioactivity – Heat produced by radioactive decay; this was a process unknown to science for decades to come.
b) Convection – The transfer of heat not through radiation or heat-conduction but through the movement of hot parts to the surface; this is a process familiar in home cooking.
An understanding of our fundamental limitations is among the most important contributions of science and of mathematics. At the same time, various fundamental limitations stated by many great minds turned out to be wrong, sometimes rather quickly.
There are quite a few cases where things that were considered to be impossible turned out to be possible. Immanuel Kant claimed: “No finite Reason can hope to understand the production of even a blade of grass by mere mechanical causes.” This quote is from the Critique of Judgment (1790). Elsewhere Kant wrote: “It is absurd to hope that another Newton will arise in the future who shall make comprehensible by us the production of a blade of grass according to natural laws which no design has ordered.”
Auguste Comte claimed: “Of all objects, the planets are those which appear to us under the least varied aspect. We see how we may determine their forms, their distances, their bulk, and their motions, but we can never know anything of their chemical or mineralogical structure; and, much less, that of organized beings living on their surface …” (The Positive Philosophy, Book II, Chapter 1 (1842)).
Spectroscopy was developed by Gustav Kirchhoff in the 1840s, and the first spectroscopic analysis of the sun appeared about ten years later, less than 20 years after Comte’s statement.