History of Niels Henrik Abel

Sejak liburan lebaran yang lalu saya sedang meluangkan waktu untuk belajar rekreasi matematika. Topik yang saya pelajari adalah aljabar (abstract algebra dan geometric/clifford algebra). Saya sebut rekreasi karena kedua topik ini bukan topik yang sehari-hari ditemukan di informatika tapi sedikit banyak mendukung dalam bidang yang sedang saya gali yaitu grafika komputer. Walau seringkali merasa jengah dengan cara penyampaian matematika yang rigorous sehingga lebih sering membuat ngantuk daripada ngerti.😀 bahkan untuk buku “Elements of Abstract and Linear Algebra”-nya E.H. Connell yang cuma 146 halaman pun cukup susah dicerna bagi saya. alhasil, saya coba mencari literatur yang relatif mudah dicerna. Setelah bongkar-bongkar katalog buku matematik yang judulnya ‘mengerikan’, akhirnya dapat buku yang bisa dinikmati yaitu ‘A First Course in Abstract Algebra’ karangan JB Fraleigh. Penyampaian buku ini sangat asik, mudah dicerna seperti buku umum, banyak contoh sederhana dan pembuktian teorema tidak terlalu di-abuse (hehehe) dan lagi ada catatan sejarah tentang suatu definisi yang membuat menarik. Salah satu catatan yang inspiratif adalah sewaktu saya membaca tentang Grup yang disebut abelian. Begini ceritanya

Commutative group are called abelian in honor of the Norwegian mathematician Niels Henrik Abel (1802-1829). Abel was interested in the question of solvability of polynomial equations. In a paper written in 1828, he proved that if all the roots of such an equation can be expressed as rational functions f, g, …, h of one of them , say x, and if for any two of these roots, f(x) and g(x) the relation f(g(x)) = g(f(x)) always holds, then the equations is solvable by radicals. Abel showrd that each of these functions in fact permutes the roots of the equation; hence, these functions are elements of the group of permutations of the roots. It was this property of commutativity in these permutation groups associated with solvable equation that led Camille Jordan in his 1870 treatise on algebra to name such groups as abelian; the name since then has been applied to commutative group in general.

Abel was attracted to mathematics as a teenager and soon surpassed all his teachers in Norway. He finally received a government travel grant to study elsewhere in 1825 and proceeded to Berlin, where he befriended August Crelle, the founder of the most influential German mathematical journal. Abel contributes numerous papers to Crell’e Journal during the next several years, including many in the field of elliptic functions, whose theory he created virtually single-handedly. Abel returned to Norway in 1827 with no position and an abundance of debts. He nevertheless continued to write brilliant papers, but died of tuberculosis at the age of 26, two days before Crelle succeeded in finding an university position for him in Berlin.

tragis.

4 comments

  1. glubot · Oktober 17, 2008

    Hmm..saya kira saya bisa mbaca pndapat lbh lanjut ttng abel dr seorang ahli informatik.
    teorema itu mmang spektakuler (Sderhana,tp dalam) n konon dkembangkan wiles u/ mbuktikan FLT
    ada buku ttng abel yg jg saya baca sbg rekreasi.hmm..lupa -_-

  2. yaniwid · Oktober 21, 2008

    Ya Peb, membaca cerita sejarah seperti ini biasanya membantu kita untuk lebih paham dan lebih tertarik. Mungkin karena kita mulai merasa ‘kenal’…

  3. dikshie · Oktober 26, 2008

    ada sekumpulang orang-orang di Cambridge University dibidang Interdomain routing (mis: BGP) yang menggunakan abstract algebra untuk memodelkan Interdomain routing (beserta artribut policies nya)

  4. contoh surat mundur kerja · Februari 3, 2014

    Hey would you mind sharing which blog platform you’re
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    The reason I ask is because your layout seems different
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    P.S Apologies for being off-topic but I had to ask!

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