Ðe Germanic Numbering System:

Note: "Gmc." = "Germanic"
"*" = unattested, reconstructed
# Indogermanic Proto-Gmc. Gothic Old English Old Norse
1 *oinos *ainaz ains ân einn, ein, eitt
2 *d(u)wôw *twôu twai twœyen (twâ, tû) tveir (tvær, tvau)
3 *treyes *þrejiz þreis þrîe (þrîo, þrîo) þrîr (þrjâr, þrjû)
4 *kwetwôres *fedwôr(iz) fidwor fêower fjôrir (fjôrar, fjogur)
5 *penkwe *femfi fimf fîf fimm
6 *s(w)eks *sehs saíhs siex sex
7 *septm > *sepunt *sebun(þ) sibun siofun sjau
8 *oktôw *ahtôu ahtau eahta átta
9 *newn > *newunt *newun(þ) niun nigun níu
10 *dekmt > *dekunt *tehun(þ) taíhun tîen(e) tíu
11 *oin- + *likw- *ain-lif ainlif endleofan ellifu
12 *dwôw + *likw- *twôu-lif twalif twelf tólf
13 *þreji-tehun(þ) *þreitaíhun þrîetîene þrettán
14 *fedwôr-tehun(þ) fidwortaíhun fêowertîene fjórtán
15 *femf-tehun(þ) fimftaíhun fîftîene fimmtán
16 *sehs-tehun(þ) *saíhstaíhun siextîene sextán
17 *sebun-tehun(þ) *sibuntaíhun siofuntîene sjaután
18 *ahtôu-tehun(þ) *ahtautaíhun eahtatîene átán
19 *newunþ-tehun(þ) *niuntaíhun niguntîene nítján

Indogermanic forms of the decades 20-90 were based on the unit number (1-9) plus a variant (d)komt- of the word for "10" (*dekmt):

Early Developments: Indogermanic to Proto-Germanic ("*" alone means "was lost")

# Indogermanic Early Proto-Germanic Late Proto-Germanic Pre-Gothic West Germanic (Pre-
Old High German)
20 *wîkmt *wî-hund
  (*wî- < *dwî- "2")
* * *
30 *tríkomt *þrí-hand * * *
40 *kwetwrkomt *fedwur-hand * * *
50 *penkwêkomt *fimfê-hand *fimfê-hund * *
60 *s(w)ekskomt *sehs-kand *sehsê-hund * *
70 *septmkomt *seftun-hand *sebuntê-hund *sibun=têhund *sebun=tô(hund)
80 *oktôkomt *ahtô-hand *ahtô-hund *ahtô=têhund *ahtô(hund)
90 *newnkomt *newun-hand *ne(w)un-hund *niun=têhund *niun=tô(hund)
100 *(d)kmtóm *hundan *hund *tehunþ=têhund *hund-tehunþ-tiy

Later Developments: Proto-Germanic to Gothic, Old English and Old Norse

(Note: The Proto-Germanic plural of *tehun "10" is *tigus "10s.")

20 through 60:

# Indogermanic Proto-Germanic Gothic Old English Old Norse
20 *dwôw + *dekús *twôu *tigus twai tigjus twœn-tiy tuttugu
30 *treyes + *dekús *þrejiz *tigus þreis tigjus þrî-tiy þrír tigir
40 '4' + *dekús *fedwôr *tigus fidwor tigjus fêower-tiy fjórir tigir
50 '5' + *dekús *femfi *tigus fimf tigjus fîf-tiy fimm tigir
60 '6' + *dekús *sehs *tigus saíhs tigjus siex-tiy sex tigir

70 through 90 with different pattern-levelings:

# Proto-Germanic Gothic Old English Old Norse
70 *sibun=têhund sibun=têhund hund-siofun-tiy sjau tigir
80 *ahtô=têhund ahtau=têhund hund-eahta-tiy átta tigir
90 niun=têhund niun=têhund hund-nigun-tiy níu tigir


# Indogermanic Proto-Germanic Gothic Old English Old Norse
100 *dekmkómt
> *(d)kmkóm(t)
  > *kmkóm
    > *kmtóm
*hundan "120" taíhun=têhund (once)
taíhun=taíhund (3x)
tíu tigir
tí-rætt hund-rað
(pl.: hund-ruð)
110 ellifu-tigir
120 *hundan "120" *hund hund-twelf-tiy tólf-rætt hund-rað
200 twa hunda twa hund,
tu hund
hund-rað ok
  átta tigir
(= 120 + 80)
240 tvau hund-ruð
300 þrija hunda þrîe-hund
360 þrjú hund-ruð
400 fidwor hunda fêower-hund
480 fjogur hund-ruð
500 fimf hunda fîf-hund
600 fimm hund-ruð
600 saíhs hunda siex-hund
720 sex hund-ruð
700 sibun hunda siofun-hund
840 sjau hund-ruð
800 ahtau hunda eahta-hund
960 átta hund-ruð
900 niun hunda nigun-hund
1,080 níu hund-ruð
1,200 tíu hund-ruð
1,320 ellifu hund-ruð
Et cetera


(Proto-Indogermanic *tûs = "strong")
# Indogermanic Early Proto-Germanic Late Proto-Germanic
1000 *tûs-(d)kmtóm *þûs-hundan *þûs-hundi

# Gothic Old English Old Norse
1,000 þûsundi þûsend
1,200 þúsund, þús-hund, þús-hund-rað
2,000 twos þûsundjos twa þûsend
2,400 tvær þûsundir
3,000 þreis þûsundjos þrîe þûsend
3,600 þrjár þûsundir
4,000 fidwor þûsundjos fêower-þûsend
4,800 fjórar þûsundir
5,000 fimf þûsundjos fîf-þûsend
6,000 fimm þûsundir, fimtán tigir hundruð
6,000 saíhs þûsundjos siex-þûsend
7,200 sex þûsundir
7,000 sibun þûsundjos siofun-þûsend
8,400 sjáu þûsundir
8,000 ahtau þûsundjos eahta-þûsend
9,600 átta þûsundir
9,000 niun þûsundjos nigun-þûsend
10,800 níu þûsundir
10,000 taíhun þûsundjos têon-þûsend
12,000 tíu þûsundir
20,000 twai tigjus þûsundjo twœn-tiy þûsend
24,000 tuttugu þûsundir
Et cetera.

Note: In the Germanic numeric vocabulary, there are three separate numbering systems:

  1. The dominant one is, as in all Indogermanic languages, the decimal system, based on 10.
  2. In addition, the Babylonian-Assyrian duodecimal system, based on 12, 60 and 120, appears in the pattern changes following the terms for "12" and "60," and in the absence of a simple word for the decimal "100." This resulted from the long contact of the Goths with the neighboring Sassanid Persians in the early centuries of our era (very roughly, 150-375 C.E.).
  3. Finally, the old "dual" form of the numeral for "8" (Gothic "ahtau"), as well as the etymology of this word (the Proto-Indogermanic root "*ok-" means "point, tip") indicates an apparently very primitive method of counting on one's fingertips (without the thumb).
Although most of us do not realize it, the numbering system we use is actually rather recent – less than a thousand years old.  The ancients used letters for numbers.  The Romans, as you probably already know, used the letters I, V, X, L, C and M in various arrangements and configurations.  The Goths, who developed their own alphabet from a mixture of runes and Greek letters around 350 C.E., used the Greek alphanumeric system as the pattern for their own.  It was:
A 1 ahsa "axis, axle"
B 2 bairkan "birch seedling"
G 3 giba "giving; that which is given, gift, present"
D 4 dags "day"
E 5 aíhvs "horse"
Q 6 qaírþra "lure, bait, decoy"
Z 7 azêti "ease, comfort, pleasureableness"
H 8 hagl "hail"
Þ 9 þiuþ "(the) good, something good."   The Gothic letter “thorn” was written like the Greek “psi”, Y, not runic þ
I 10 eis "ice"
K 20 kusma "boil, tumefaction, infected swelling"
L 30 lagus "lake, sea, open water, ocean"
M 40 manna "man, human being"
N 50 nauþs "necessitation, compulsion, force, constraint; duress"
J 60 jêr "year."   Written something like “G,” but pronounced as English “y” in “year” or the “K” in “OK” when slurred as “Ogay.”
U 70 ûrus "urus, aurochs," extinct European bison
P 80 paírþra "dice cup, dice box, cup for throwing dice"
q 90 Koppa;  used only as a number, never as a letter
R 100 raida "ride, journey; riding vehicle, wagon"
S 200 sáuïl sun
T 300 Teiws "Tew, Tyr, Tiu or Ziu," before Wodan's time, the highest divinity, the one-armed god of the sky and war (and god of "Tue's day"); = Roman Mars.
W 400 winja "pasture, grazing meadow."   Written like a capital “Y”
F 500 faíhu "movable goods, chattels; property, possessions; wealth, riches; money"
X 600 Iggws [Originally NG-rune] "Ingw," a Germanic demigod, myhical progenitor of the Anglo-Frisian Ingwaeones
Hv 700 hvaír "cauldron."   Written like the Greek “theta,” Q
O 800 ôþal "patrimony, ancestral inheritance"
á 900 Teiws "Tew" The RUNE Teiws or Tyr (see "T," above);  written as an upward-pointing arrow.  Not used as a letter.

The key concept in the development of modern arithmetic and mathematics was the concept of zero.

The philosophical preparation for the concept of zero was laid in the Middle Ages by the Christian schoolmen who, following Aristotle, viewed the world as being composed of “form” (forma) without “substance” (materia).  During the crusades, the Latin West borrowed not only Greek philosophy from the Mohammedans (who had translated it into Arabic), but also the Sanskrit numbering system.  That is, the numerals we currently use came from the "Indo-" part of the Indogermanic-speaking peoples.  For the Muslims had conquered northern India and adopted the mathematics originally invented and used there, whence they took these numerals to the west.  Europeans came in contact with them during the crusades.  As a result, the “Arabic” numerals 0 1 2 3 4 5 6 7 8 9 are in actual fact not Arabic at all, but Sanskrit and Indic.  Europeans then took this Arabic-overlayed Sanskritic mathematics (“algebra,” “zero” and “algorithm,” like “alchemy” and “chemistry,” are Arabic words) and, combining it with Graeco-Roman philosophy which viewed the universe as essentially rational, began to develop mathematics as we know it in the West today - a mathematics which is the foundation of science.  “Zero” (same word as “cipher”) was viewed as pure “form” without substance, whereas the other digits were thought of as various levels of form with substance.  This made modern calculations possible (Imagine having to multiply and divide with Roman numerals!).  Our history, thus, is a history of the synthesis of ideas.  We take the best ideas from any and every source and combine them with the best ideas from elsewhere, thereby creating new intellectual structures much more powerful than any of its components.  No other branch of man has come anywhere close to us in this respect.

— Þeedrich = (reachable at theedrich@harbornet.com)