Enjoying Science Requires Effort

When you have reached and entered the gates of science, how are you to use and enjoy this new and beautiful land? This is a very important question for you may make a twofold use of it. If you are only ambitious to shine in the world, you may use it chiefly to get prizes, to be at the top of your class, or to pass in examinations; but if you also enjoy discovering its secrets, and desire to learn more and more of nature and to revel in dreams of its beauty, then you will study science for it...

 Conjecture versus Theorem

Mathematicians use the idea of proof to make a distinction between a 'conjecture' and a 'theorem', which bears a superficial resemblance to the OED's distinction between the two senses of 'theory'. A conjecture is a proposition that looks true but has never been proved. It will become a theorem when it has been proved. A famous example is the Goldbach Conjecture, which states that any even integer can be expressed as the sum of two primes. Mathematicians have failed to disprove it for all eve...