Fermat's Last Theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem


00:00:11 1 Overview
00:01:26 1.1 Pythagorean origins
00:01:34 1.2 Subsequent developments and solution
00:01:46 1.3 Equivalent statements of the theorem
00:02:46 2 Mathematical history
00:07:01 2.1 Pythagoras and Diophantus
00:08:12 2.1.1 Pythagorean triples
00:09:36 2.1.2 Diophantine equations
00:09:51 2.2 Fermat's conjecture
00:10:37 2.3 Proofs for specific exponents
00:11:01 2.3.1 Exponent = 4
00:11:48 2.3.2 Other exponents
00:11:58 2.3.3 Sophie Germain
00:12:07 2.3.4 Ernst Kummer and the theory of ideals
00:12:34 2.3.5 Mordell conjecture
00:13:38 2.3.6 Computational studies
00:14:55 2.4 Connection with elliptic curves
00:15:39 2.4.1 Taniyama–Shimura–Weil conjecture
00:15:45 2.4.2 Ribet's theorem for Frey curves
00:15:54 2.4.3 Wiles's general proof
00:16:12 2.5 Subsequent developments
00:17:08 3 Exponents other than positive integers
00:18:17 3.1 Reciprocal integers (inverse Fermat equation)
00:18:27 3.2 Rational exponents
00:19:12 3.3 Negative exponents
00:19:31 3.3.1 in/i =&#160;–1
00:20:43 3.3.2 in/i =&#160;–2
00:20:53 3.3.3 Integer in/i &lt;&#160;–2
00:21:38 4 Base values other than positive integers
00:22:20 5 Monetary prizes
00:22:41 6 In popular culture
00:23:56 7 See also
00:24:32 8 Footnotes
00:24:45 9 References
00:25:09 10 Bibliography
00:26:00 11 Further reading
00:26:21 12 External links
00:28:13 Ernst Kummer and the theory of ideals
00:30:03 Mordell conjecture
00:30:29 Computational studies
00:31:26 Connection with elliptic curves
00:32:07 Taniyama–Shimura–Weil conjecture
00:33:24 Ribet's theorem for Frey curves
00:36:01 Wiles's general proof
00:41:22 Subsequent developments
00:41:55 3 was already known by Euler.)
00:41:59 Exponents other than positive integers
00:42:10 === Reciprocal integers (inverse Fermat equation)
00:43:34 Rational exponents
00:44:41 Negative exponents
00:44:50 n = –1
00:46:05 n = –2
00:48:20 Integer n  –2
00:48:45 Base values other than positive integers
00:49:57 Monetary prizes
00:52:01 In popular culture
00:53:23 See also



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SUMMARY
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In number theory Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known to have infinitely many solutions since antiquity.This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The proof was described as a 'stunning advance' in the citation for his Abel Prize award in 2016. The proof of Fermat's Last Theorem also proved much of the modularity theorem and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques.
The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof, it was in the Guinness Book of World Records as the "most difficult mathematical problem", one of the reasons being that it has the largest number of unsuccessful proofs.