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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Numeral system predating modern Hindu-Arabic numerals</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Evolution_of_Brahmi_numerals.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Evolution_of_Brahmi_numerals.jpg/260px-Evolution_of_Brahmi_numerals.jpg" decoding="async" width="260" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Evolution_of_Brahmi_numerals.jpg/390px-Evolution_of_Brahmi_numerals.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Evolution_of_Brahmi_numerals.jpg/520px-Evolution_of_Brahmi_numerals.jpg 2x" data-file-width="1543" data-file-height="887" /></a><figcaption>Evolution of Brahmi numerals from the time of Ashoka.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ashoka_Brahmi_numerals_256.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Ashoka_Brahmi_numerals_256.jpg/110px-Ashoka_Brahmi_numerals_256.jpg" decoding="async" width="110" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Ashoka_Brahmi_numerals_256.jpg/165px-Ashoka_Brahmi_numerals_256.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Ashoka_Brahmi_numerals_256.jpg/220px-Ashoka_Brahmi_numerals_256.jpg 2x" data-file-width="1144" data-file-height="1031" /></a><figcaption>The number "256" in Ashoka's <a href="/wiki/Minor_Rock_Edict" class="mw-redirect" title="Minor Rock Edict">Minor Rock Edict</a> No.1 in <a href="/wiki/Sasaram" title="Sasaram">Sasaram</a> (circa 250 BCE).</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Western_Satrap_Damasena_year_153.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Western_Satrap_Damasena_year_153.jpg/220px-Western_Satrap_Damasena_year_153.jpg" decoding="async" width="220" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Western_Satrap_Damasena_year_153.jpg/330px-Western_Satrap_Damasena_year_153.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Western_Satrap_Damasena_year_153.jpg/440px-Western_Satrap_Damasena_year_153.jpg 2x" data-file-width="1004" data-file-height="510" /></a><figcaption>Coin of <a href="/wiki/Western_Satrap" class="mw-redirect" title="Western Satrap">Western Satrap</a> <a href="/wiki/Damasena" title="Damasena">Damasena</a> (232 CE). The minting date, here 153 (100-50-3 in <a href="/wiki/File:Brahmi_numeral_signs.svg" title="File:Brahmi numeral signs.svg">Brahmi script numerals</a>) of the <a href="/wiki/Saka_era" class="mw-redirect" title="Saka era">Saka era</a>, therefore 232 CE, clearly appears behind the head of the king.</figcaption></figure> <p><b>Brahmi numerals</b> are a <a href="/wiki/Numeral_system" title="Numeral system">numeral system</a> attested in the <a href="/wiki/Indian_subcontinent" title="Indian subcontinent">Indian subcontinent</a> from the 3rd century BCE. It is the direct graphic ancestor of the modern <a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numeral system</a>. However, the Brahmi numeral system was conceptually distinct from these later systems, as it was a non-<a href="/wiki/Positional_notation" title="Positional notation">positional</a> decimal system, and did not include <a href="/wiki/0_(number)" class="mw-redirect" title="0 (number)">zero</a>. Later additions to the system included separate symbols for each multiple of 10 (e.g. 20, 30, and 40). There were also symbols for 100 and 1000, which were combined in <a href="/wiki/Typographic_ligature" class="mw-redirect" title="Typographic ligature">ligatures</a> with the units to signify 200, 300, 2000, 3000, etc. In computers, these ligatures are written with the Brahmi Number Joiner at U+1107F. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Origins">Origins</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmi_numerals&action=edit&section=1" title="Edit section: Origins"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Brahmi_numeral_signs.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Brahmi_numeral_signs.svg/350px-Brahmi_numeral_signs.svg.png" decoding="async" width="350" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Brahmi_numeral_signs.svg/525px-Brahmi_numeral_signs.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Brahmi_numeral_signs.svg/700px-Brahmi_numeral_signs.svg.png 2x" data-file-width="613" data-file-height="291" /></a><figcaption>Brahmi numerals signs of the 2nd century CE.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul 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a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Numeral_systems" title="Category:Numeral systems">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Numeral_system" title="Numeral system">Numeral systems</a></th></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Positional_notation" title="Positional notation">Place-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numerals</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Arabic_numerals" title="Arabic numerals">Western Arabic</a></li> <li><a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic</a></li></ul> <hr /> <ul><li><a href="/wiki/Bengali_numerals" title="Bengali numerals">Bengali</a></li> <li><a href="/wiki/Devanagari_numerals" title="Devanagari numerals">Devanagari</a></li> <li><a href="/wiki/Gujarati_numerals" title="Gujarati numerals">Gujarati</a></li> <li><a href="/wiki/Gurmukhi_numerals" class="mw-redirect" title="Gurmukhi numerals">Gurmukhi</a></li> <li><a href="/wiki/Odia_numerals" title="Odia numerals">Odia</a></li> <li><a href="/wiki/Sinhala_numerals" title="Sinhala numerals">Sinhala</a></li> <li><a href="/wiki/Tamil_numerals" title="Tamil numerals">Tamil</a></li> <li><a href="/wiki/Malayalam_numerals" title="Malayalam numerals">Malayalam</a></li> <li><a href="/wiki/Telugu_script#Numerals" title="Telugu script">Telugu</a></li> <li><a href="/wiki/Kannada_script#Numerals" title="Kannada script">Kannada</a></li> <li><a href="/wiki/Dzongkha_numerals" title="Dzongkha numerals">Dzongkha</a></li></ul> <hr /> <ul><li><a href="/wiki/Tibetan_numerals" title="Tibetan numerals">Tibetan</a></li> <li><a href="/wiki/Balinese_numerals" title="Balinese numerals">Balinese</a></li> <li><a href="/wiki/Burmese_numerals" title="Burmese numerals">Burmese</a></li> <li><a href="/wiki/Javanese_numerals" title="Javanese numerals">Javanese</a></li> <li><a href="/wiki/Khmer_numerals" title="Khmer numerals">Khmer</a></li> <li><a href="/wiki/Lao_script#Numerals" title="Lao script">Lao</a></li> <li><a href="/wiki/Mongolian_numerals" title="Mongolian numerals">Mongolian</a></li> <li><a href="/wiki/Sundanese_numerals" title="Sundanese numerals">Sundanese</a></li> <li><a href="/wiki/Thai_numerals" title="Thai numerals">Thai</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">East Asian systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese</a> <ul><li><a href="/wiki/Suzhou_numerals" title="Suzhou numerals">Suzhou</a></li></ul></li> <li><a href="/wiki/Hokkien_numerals" title="Hokkien numerals">Hokkien</a></li> <li><a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese</a></li> <li><a href="/wiki/Korean_numerals" title="Korean numerals">Korean</a></li> <li><a href="/wiki/Vietnamese_numerals" title="Vietnamese numerals">Vietnamese</a></li></ul> <hr /> <dl><dt>Historic</dt></dl> <ul><li><a href="/wiki/Counting_rods" title="Counting rods">Counting rods</a></li> <li><a href="/wiki/Tangut_numerals" title="Tangut numerals">Tangut</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Other systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">History</a></li></ul> <hr /> <dl><dt><a href="/wiki/Ancient_history" title="Ancient history">Ancient</a></dt></dl> <ul><li><a href="/wiki/Babylonian_cuneiform_numerals" title="Babylonian cuneiform numerals">Babylonian</a></li></ul> <hr /> <dl><dt><a href="/wiki/Post-classical_history" title="Post-classical history">Post-classical</a></dt></dl> <ul><li><a href="/wiki/Cistercian_numerals" title="Cistercian numerals">Cistercian</a></li> <li><a href="/wiki/Maya_numerals" title="Maya numerals">Mayan</a></li> <li><a href="/wiki/Muisca_numerals" title="Muisca numerals">Muisca</a></li> <li><a href="/wiki/Pentadic_numerals" title="Pentadic numerals">Pentadic</a></li> <li><a href="/wiki/Quipu" title="Quipu">Quipu</a></li> <li><a href="/wiki/Rumi_Numeral_Symbols" title="Rumi Numeral Symbols">Rumi</a></li></ul> <hr /> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Cherokee_syllabary#Numerals" title="Cherokee syllabary">Cherokee</a></li> <li><a href="/wiki/Kaktovik_numerals" title="Kaktovik numerals">Kaktovik</a> (Iñupiaq)</li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">By <a href="/wiki/Radix" title="Radix">radix/base</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Common radices/bases</dt></dl> <ul><li><a href="/wiki/Binary_number" title="Binary number">2</a></li> <li><a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">3</a></li> <li><a href="/wiki/Quaternary_numeral_system" title="Quaternary numeral system">4</a></li> <li><a href="/wiki/Quinary" title="Quinary">5</a></li> <li><a href="/wiki/Senary" title="Senary">6</a></li> <li><a href="/wiki/Octal" title="Octal">8</a></li> <li><a href="/wiki/Decimal" title="Decimal">10</a></li> <li><a href="/wiki/Duodecimal" title="Duodecimal">12</a></li> <li><a href="/wiki/Hexadecimal" title="Hexadecimal">16</a></li> <li><a href="/wiki/Vigesimal" title="Vigesimal">20</a></li> <li><a href="/wiki/Sexagesimal" title="Sexagesimal">60</a></li></ul> <hr /> <dl><dt><a href="/wiki/Non-standard_positional_numeral_systems" title="Non-standard positional numeral systems">Non-standard radices/bases</a></dt></dl> <ul><li><a href="/wiki/Bijective_numeration" title="Bijective numeration">Bijective</a><span class="nowrap"> </span>(<a href="/wiki/Unary_numeral_system" title="Unary numeral system">1</a>)</li> <li><a href="/wiki/Signed-digit_representation" title="Signed-digit representation">Signed-digit</a><span class="nowrap"> </span>(<a href="/wiki/Balanced_ternary" title="Balanced ternary">balanced ternary</a>)</li> <li><a href="/wiki/Mixed_radix" title="Mixed radix">Mixed</a><span class="nowrap"> </span>(<a href="/wiki/Factorial_number_system" title="Factorial number system">factorial</a>)</li> <li><a href="/wiki/Negative_base" title="Negative base">Negative</a></li> <li><a href="/wiki/Complex-base_system" title="Complex-base system">Complex</a><span class="nowrap"> </span>(<a href="/wiki/Quater-imaginary_base" title="Quater-imaginary base">2<i>i</i></a>)</li> <li><a href="/wiki/Non-integer_base_of_numeration" title="Non-integer base of numeration">Non-integer</a><span class="nowrap"> </span>(<a href="/wiki/Golden_ratio_base" title="Golden ratio base">φ</a>)</li> <li><a href="/wiki/Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric</a></li></ul></div></div></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Sign-value_notation" title="Sign-value notation">Sign-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Non-alphabetic</dt></dl> <ul><li><a href="/wiki/Aegean_numerals" title="Aegean numerals">Aegean</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic</a></li> <li><a href="/wiki/Aztec_script#Numerals" title="Aztec script">Aztec</a></li> <li><a class="mw-selflink selflink">Brahmi</a></li> <li><a href="/wiki/Chuvash_numerals" title="Chuvash numerals">Chuvash</a></li> <li><a href="/wiki/Egyptian_numerals" title="Egyptian numerals">Egyptian</a></li> <li><a href="/wiki/Etruscan_numerals" title="Etruscan numerals">Etruscan</a></li> <li><a href="/wiki/Kharosthi_numerals" class="mw-redirect" title="Kharosthi numerals">Kharosthi</a></li> <li><a href="/wiki/Prehistoric_counting" title="Prehistoric counting">Prehistoric counting</a></li> <li><a href="/wiki/Proto-cuneiform" title="Proto-cuneiform">Proto-cuneiform</a></li> <li><a href="/wiki/Roman_numerals" title="Roman numerals">Roman</a></li> <li><a href="/wiki/Tally_marks" title="Tally marks">Tally marks</a></li></ul> <hr /> <dl><dt><a href="/wiki/Alphabetic_numeral_system" title="Alphabetic numeral system">Alphabetic</a></dt></dl> <ul><li><a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad</a></li> <li><a href="/wiki/Armenian_numerals" title="Armenian numerals">Armenian</a></li> <li><a href="/wiki/Alphasyllabic_numeral_system" title="Alphasyllabic numeral system">Alphasyllabic</a> <ul><li><a href="/wiki/Aksharapalli" title="Aksharapalli">Akṣarapallī</a></li> <li><a href="/wiki/%C4%80ryabha%E1%B9%ADa_numeration" title="Āryabhaṭa numeration">Āryabhaṭa</a></li> <li><a href="/wiki/Katapayadi_system" title="Katapayadi system">Kaṭapayādi</a></li></ul></li> <li><a href="/wiki/Coptic_numerals" class="mw-redirect" title="Coptic numerals">Coptic</a></li> <li><a href="/wiki/Cyrillic_numerals" title="Cyrillic numerals">Cyrillic</a></li> <li><a href="/wiki/Ge%CA%BDez_script#Numerals" title="Geʽez script">Geʽez</a></li> <li><a href="/wiki/Georgian_numerals" title="Georgian numerals">Georgian</a></li> <li><a href="/wiki/Glagolitic_numerals" title="Glagolitic numerals">Glagolitic</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek</a></li> <li><a href="/wiki/Hebrew_numerals" title="Hebrew numerals">Hebrew</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <a href="/wiki/List_of_numeral_systems" title="List of numeral systems">List of numeral systems</a></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Numeral_systems" title="Template:Numeral systems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Numeral_systems" title="Template talk:Numeral systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Numeral_systems" title="Special:EditPage/Template:Numeral systems"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The source of the first three numerals seems clear: they are collections of 1, 2, and 3 strokes, in <a href="/wiki/Ashoka" title="Ashoka">Ashoka</a>'s era vertical I, II, III like <a href="/wiki/Roman_numeral" class="mw-redirect" title="Roman numeral">Roman numerals</a>, but soon becoming horizontal like the <a href="/wiki/Chinese_numerals" title="Chinese numerals">Han Chinese numerals</a>. In the oldest inscriptions, 4 looks like a +, reminiscent of the X of neighboring <a href="/wiki/Kharosthi#Numerals" title="Kharosthi"><span title="International Alphabet of Sanskrit transliteration"><i lang="sa-Latn">Kharoṣṭhī</i></span></a>, and perhaps a representation of 4 lines or 4 directions. However, the other unit numerals appear to be arbitrary symbols in even the oldest inscriptions.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2014)">citation needed</span></a></i>]</sup> It is sometimes supposed that they may also have come from collections of strokes, run together in cursive writing in a way similar to that attested in the development of Egyptian <a href="/wiki/Hieratic" title="Hieratic">hieratic</a> and <a href="/wiki/Demotic_(Egyptian)" title="Demotic (Egyptian)">demotic</a> numerals, but this is not supported by any direct evidence. Likewise, the units for the tens are not obviously related to each other or to the units, although 10, 20, 80, 90 might be based on a circle.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2024)">citation needed</span></a></i>]</sup> </p><p>The sometimes rather striking graphic similarity they have with the hieratic and demotic Egyptian numerals, while suggestive, is not prima facie evidence of an historical connection, as many cultures have independently recorded numbers as collections of strokes. With a similar writing instrument, the cursive forms of such groups of strokes could easily be broadly similar as well, and this is one of the primary hypotheses for the origin of Brahmi numerals.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2024)">citation needed</span></a></i>]</sup> </p><p>Another possibility is that the numerals were <a href="/wiki/Acrophony" title="Acrophony">acrophonic</a>, like the <a href="/wiki/Attic_numerals" title="Attic numerals">Attic numerals</a>, and based on the <span title="International Alphabet of Sanskrit transliteration"><i lang="sa-Latn"><a href="/wiki/Kharo%E1%B9%A3%E1%B9%ADh%C4%AB" class="mw-redirect" title="Kharoṣṭhī">Kharoṣṭhī</a></i></span> alphabet. For instance, 4 "chatur" early on took a shape much like the Kharosthi letter 𐨖 "ch", while 5 "pancha" looks remarkably like Kharosthi 𐨤 "p"; and so on through 6 "ssat" and 𐨮, then 7 "sapta" and 𐨯, and finally 9 <i>nava</i> and 𐨣. However, there are problems of timing and lack of records. The full set of numerals is not attested until the 1st-2nd century CE, 400 years after Ashoka. Assertions that either the numerals derive from tallies or that they are alphabetic are, at best, educated guesses.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2024)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Numerals">Numerals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmi_numerals&action=edit&section=2" title="Edit section: Numerals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <caption>Ancient non-Zero system </caption> <tbody><tr> <th>Hindu–Arabic numerals </th> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td>10</td> <td>20</td> <td>30</td> <td>40</td> <td>50</td> <td>60</td> <td>70</td> <td>80</td> <td>90</td> <td>100</td> <td>1000 </td></tr> <tr> <th>Brahmi numerals </th> <td>𑁒</td> <td>𑁓</td> <td>𑁔</td> <td>𑁕</td> <td>𑁖</td> <td>𑁗</td> <td>𑁘</td> <td>𑁙</td> <td>𑁚</td> <td>𑁛</td> <td>𑁜</td> <td>𑁝</td> <td>𑁞</td> <td>𑁟</td> <td>𑁠</td> <td>𑁡</td> <td>𑁢</td> <td>𑁣</td> <td>𑁤</td> <td>𑁥 </td></tr></tbody></table> <table class="wikitable"> <caption>Zero place-holder system </caption> <tbody><tr> <th>Hindu–Arabic numerals </th> <td>0</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9 </td></tr> <tr> <th>Brahmi numerals </th> <td>𑁦</td> <td>𑁧</td> <td>𑁨</td> <td>𑁩</td> <td>𑁪</td> <td>𑁫</td> <td>𑁬</td> <td>𑁭</td> <td>𑁮</td> <td>𑁯 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmi_numerals&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Brahmi_script" title="Brahmi script">Brahmi script</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brahmi_numerals&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> </div> <ul><li>Georges Ifrah, <i>The Universal History of Numbers: From Prehistory to the Invention of the Computer.</i> Translated by David Bellos, Sophie Wood, pub. J. Wiley, 2000.</li> <li><a href="/wiki/Karl_Menninger_(mathematics)" title="Karl Menninger (mathematics)">Karl Menninger (mathematics)</a>, <i>Number Words and Number Symbols - A Cultural History of Numbers</i> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-27096-3" title="Special:BookSources/0-486-27096-3">0-486-27096-3</a> <a rel="nofollow" class="external autonumber" href="https://books.google.com/books?id=BFJHzSIj2u0C&dq=Wagner+%22Bamberg+Arithmetic%22&pg=PA393">[1]</a></li> <li><a href="/wiki/David_Eugene_Smith" title="David Eugene Smith">David Eugene Smith</a> and <a href="/wiki/Louis_Charles_Karpinski" title="Louis Charles Karpinski">Louis Charles Karpinski</a>, <i>The Hindu–Arabic Numerals</i> (1911) <a rel="nofollow" class="external autonumber" href="https://books.google.com/books?id=eQoCAAAAYAAJ">[2]</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output 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.navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Indian_mathematics" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Indian_mathematics" 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class="navbox-group" style="width:1%">Ancient</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apastamba_Dharmasutra" title="Apastamba Dharmasutra">Apastamba</a></li> <li><a href="/wiki/Baudhayana_sutras" title="Baudhayana sutras">Baudhayana</a></li> <li><a href="/wiki/K%C4%81ty%C4%81yana" title="Kātyāyana">Katyayana</a></li> <li><a href="/wiki/Manava" title="Manava">Manava</a></li> <li><a href="/wiki/P%C4%81%E1%B9%87ini" title="Pāṇini">Pāṇini</a></li> <li><a href="/wiki/Pingala" title="Pingala">Pingala</a></li> <li><a href="/wiki/Yajnavalkya" title="Yajnavalkya">Yajnavalkya</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classical</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aryabhata" title="Aryabhata">Āryabhaṭa I</a></li> <li><a href="/wiki/Aryabhata_II" title="Aryabhata II">Āryabhaṭa II</a></li> <li><a href="/wiki/Bh%C4%81skara_I" title="Bhāskara I">Bhāskara I</a></li> <li><a href="/wiki/Bh%C4%81skara_II" title="Bhāskara II">Bhāskara II</a></li> <li><a href="/wiki/Melpathur_Narayana_Bhattathiri" title="Melpathur Narayana Bhattathiri">Melpathur Narayana Bhattathiri</a></li> <li><a href="/wiki/Brahmadeva" title="Brahmadeva">Brahmadeva</a></li> <li><a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a></li> <li><a href="/wiki/Govindasv%C4%81mi" title="Govindasvāmi">Govindasvāmi</a></li> <li><a href="/wiki/Halayudha" title="Halayudha">Halayudha</a></li> <li><a href="/wiki/Jye%E1%B9%A3%E1%B9%ADhadeva" title="Jyeṣṭhadeva">Jyeṣṭhadeva</a></li> <li><a href="/wiki/Kamalakara" title="Kamalakara">Kamalakara</a></li> <li><a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Mādhava of Saṅgamagrāma</a></li> <li><a href="/wiki/Mah%C4%81v%C4%ABra_(mathematician)" title="Mahāvīra (mathematician)">Mahāvīra</a></li> <li><a href="/wiki/Mahendra_S%C5%ABri" title="Mahendra Sūri">Mahendra Sūri</a></li> <li><a href="/wiki/Munishvara" title="Munishvara">Munishvara</a></li> <li><a href="/wiki/Narayana_Pandit" class="mw-redirect" title="Narayana Pandit">Narayana</a></li> <li><a href="/wiki/Parameshvara" class="mw-redirect" title="Parameshvara">Parameshvara</a></li> <li><a href="/wiki/Achyuta_Pisharati" class="mw-redirect" title="Achyuta Pisharati">Achyuta Pisharati</a></li> <li><a href="/wiki/Jagannatha_Samrat" title="Jagannatha Samrat">Jagannatha Samrat</a></li> <li><a href="/wiki/Nilakantha_Somayaji" title="Nilakantha Somayaji">Nilakantha Somayaji</a></li> <li><a href="/wiki/%C5%9Ar%C4%ABpati" title="Śrīpati">Śrīpati</a></li> <li><a href="/wiki/Sridhara" title="Sridhara">Sridhara</a></li> <li><a href="/wiki/Gangesha_Upadhyaya" class="mw-redirect" title="Gangesha Upadhyaya">Gangesha Upadhyaya</a></li> <li><a href="/wiki/Var%C4%81hamihira" title="Varāhamihira">Varāhamihira</a></li> <li><a href="/wiki/Sankara_Variar" title="Sankara Variar">Sankara Variar</a></li> <li><a href="/wiki/Virasena" title="Virasena">Virasena</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Srinivasa_Ramanujan" title="Srinivasa Ramanujan">Srinivasa Ramanujan</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Satyendra Nath Bose</a></li> <li><a href="/wiki/P.C._Mahalanobis" class="mw-redirect" title="P.C. Mahalanobis">P.C. Mahalanobis</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Subrahmanyan Chandrasekhar</a></li> <li><a href="/wiki/C.R._Rao" class="mw-redirect" title="C.R. Rao">C.R. Rao</a></li> <li><a href="/wiki/Veeravalli_S._Varadarajan" title="Veeravalli S. Varadarajan">Veeravalli S. Varadarajan</a></li> <li><a href="/wiki/S._R._Srinivasa_Varadhan" title="S. R. Srinivasa Varadhan">S. R. Srinivasa Varadhan</a></li> <li><a href="/wiki/K._R._Parthasarathy_(probabilist)" title="K. R. Parthasarathy (probabilist)">K. R. Parthasarathy (probabilist)</a></li> <li><a href="/wiki/M._S._Narasimhan" title="M. S. Narasimhan">M. S. Narasimhan</a></li> <li><a href="/wiki/C._S._Seshadri" title="C. S. Seshadri">C. S. Seshadri</a></li> <li><a href="/wiki/Harish-Chandra" title="Harish-Chandra">Harish-Chandra</a></li> <li><a href="/wiki/Subbayya_Sivasankaranarayana_Pillai" title="Subbayya Sivasankaranarayana Pillai">Subbayya Sivasankaranarayana Pillai</a></li> <li><a href="/wiki/Tilak_Raj_Prabhakar" title="Tilak Raj Prabhakar">Tilak Raj Prabhakar</a></li> <li><a href="/wiki/Manjul_Bhargava" title="Manjul Bhargava">Manjul Bhargava</a></li> <li><a href="/wiki/Akshay_Venkatesh" title="Akshay Venkatesh">Akshay Venkatesh</a></li> <li><a href="/wiki/Ravi_Vakil" title="Ravi Vakil">Ravi Vakil</a></li> <li><a href="/wiki/Kannan_Soundararajan" title="Kannan Soundararajan">Kannan Soundararajan</a></li> <li><a href="/wiki/Template:SSBPST_recipients_in_Mathematical_Science" title="Template:SSBPST recipients in Mathematical Science">Shanti Swarup Bhatnagar Prize recipients in Mathematical Science</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Treatises</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Aryabhatiya" title="Aryabhatiya">Aryabhatiya</a></i></li> <li><a href="/wiki/Bakhshali_manuscript" title="Bakhshali manuscript">Bakhshali manuscript</a></li> <li><i><a href="/wiki/Bijaganita" title="Bijaganita">Bijaganita</a></i></li> <li><i><a href="/wiki/Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81nta" title="Brāhmasphuṭasiddhānta">Brāhmasphuṭasiddhānta</a></i></li> <li><i><a href="/wiki/Ganita_Kaumudi" title="Ganita Kaumudi">Ganita Kaumudi</a></i></li> <li><i><a href="/wiki/Kanakkusaram" title="Kanakkusaram">Kanakkusaram</a></i></li> <li><i><a href="/wiki/Karanapaddhati" title="Karanapaddhati">Karanapaddhati</a></i></li> <li><i><a href="/wiki/L%C4%ABl%C4%81vat%C4%AB" title="Līlāvatī">Līlāvatī</a></i></li> <li><i><a href="/wiki/Lokavibhaga" title="Lokavibhaga">Lokavibhaga</a></i></li> <li><i><a href="/wiki/P%C4%81t%C4%ABga%E1%B9%87ita" title="Pātīgaṇita">Pātīgaṇita</a></i></li> <li><i><a href="/wiki/Paulisa_Siddhanta" title="Paulisa Siddhanta">Paulisa Siddhanta</a></i></li> <li><i><a href="/wiki/Var%C4%81hamihira#Pancha-Siddhantika" title="Varāhamihira">Paitamaha Siddhanta</a></i></li> <li><i><a href="/wiki/Romaka_Siddhanta" title="Romaka Siddhanta">Romaka Siddhanta</a></i></li> <li><i><a href="/wiki/Sadratnamala" title="Sadratnamala">Sadratnamala</a></i></li> <li><i><a href="/wiki/Siddh%C4%81nta_Shiromani" title="Siddhānta Shiromani">Siddhānta Shiromani</a></i></li> <li><i><a href="/wiki/Shulba_Sutras" title="Shulba Sutras">Śulba Sūtras</a></i></li> <li><i><a href="/wiki/Surya_Siddhanta" title="Surya Siddhanta">Surya Siddhanta</a></i></li> <li><i><a href="/wiki/Tantrasamgraha" title="Tantrasamgraha">Tantrasamgraha</a></i></li> <li><i><a href="/wiki/Vasishtha_Siddhanta" title="Vasishtha Siddhanta">Vasishtha Siddhanta</a></i></li> <li><i><a href="/wiki/Venvaroha" title="Venvaroha">Veṇvāroha</a></i></li> <li><i><a href="/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81" title="Yuktibhāṣā">Yuktibhāṣā</a></i></li> <li><i><a href="/wiki/Yavanajataka" title="Yavanajataka">Yavanajataka</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Pioneering<br /> innovations</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Brahmi numerals</a></li> <li><a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numeral system</a></li> <li>Symbol for <a href="/wiki/0" title="0">zero (0)</a></li> <li><a href="/wiki/Madhava_series" title="Madhava series">Infinite series expansions for the trigonometric functions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centres</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kerala_school_of_astronomy_and_mathematics" title="Kerala school of astronomy and mathematics">Kerala school of astronomy and mathematics</a></li> <li><a href="/wiki/Jantar_Mantar" title="Jantar Mantar">Jantar Mantar</a> (<a href="/wiki/Jantar_Mantar,_Jaipur" title="Jantar Mantar, Jaipur">Jaipur</a>, <a href="/wiki/Jantar_Mantar,_New_Delhi" title="Jantar Mantar, New Delhi">New Delhi</a>, <a href="/wiki/Jantar_Mantar,_Ujjain" title="Jantar Mantar, Ujjain">Ujjain</a>, <a href="/wiki/Jantar_Mantar,_Varanasi" title="Jantar Mantar, Varanasi">Varanasi</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Historians of<br /> mathematics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bapudeva_Sastri" title="Bapudeva Sastri">Bapudeva Sastri</a> (1821–1900)</li> <li><a href="/w/index.php?title=Shankar_Balakrishna_Dikshit&action=edit&redlink=1" class="new" title="Shankar Balakrishna Dikshit (page does not exist)">Shankar Balakrishna Dikshit</a> (1853–1898)</li> <li><a href="/wiki/Sudhakara_Dvivedi" title="Sudhakara Dvivedi">Sudhakara Dvivedi</a> (1855–1910)</li> <li><a href="/w/index.php?title=M._Rangacarya&action=edit&redlink=1" class="new" title="M. Rangacarya (page does not exist)">M. Rangacarya</a> (1861–1916)</li> <li><a href="/wiki/P._C._Sengupta" class="mw-redirect" title="P. C. Sengupta">P. C. Sengupta</a> (1876–1962)</li> <li><a href="/wiki/B._B._Datta" class="mw-redirect" title="B. B. Datta">B. B. Datta</a> (1888–1958)</li> <li><a href="/wiki/Takao_Hayashi" title="Takao Hayashi">T. Hayashi</a></li> <li><a href="/w/index.php?title=A._A._Krishnaswamy_Ayyangar&action=edit&redlink=1" class="new" title="A. A. Krishnaswamy Ayyangar (page does not exist)">A. A. Krishnaswamy Ayyangar</a> (1892– 1953)</li> <li><a href="/wiki/Avadhesh_Narayan_Singh" title="Avadhesh Narayan Singh">A. N. Singh</a> (1901–1954)</li> <li><a href="/wiki/C._T._Rajagopal" class="mw-redirect" title="C. T. Rajagopal">C. T. Rajagopal</a> (1903–1978)</li> <li><a href="/wiki/T._A._Saraswati_Amma" class="mw-redirect" title="T. A. Saraswati Amma">T. A. Saraswati Amma</a> (1918–2000)</li> <li><a href="/w/index.php?title=S._N._Sen&action=edit&redlink=1" class="new" title="S. N. Sen (page does not exist)">S. N. Sen</a> (1918–1992)</li> <li><a href="/wiki/K._S._Shukla" class="mw-redirect" title="K. S. Shukla">K. S. Shukla</a> (1918–2007)</li> <li><a href="/wiki/K._V._Sarma" title="K. V. Sarma">K. V. Sarma</a> (1919–2005)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Translators</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Walter_Eugene_Clark" title="Walter Eugene Clark">Walter Eugene Clark</a></li> <li><a href="/wiki/Henry_Thomas_Colebrooke" title="Henry Thomas Colebrooke">Henry Thomas Colebrooke </a></li> <li><a href="/wiki/David_Pingree" title="David Pingree">David Pingree</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other regions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylon</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">China</a></li> <li><a href="/wiki/Greek_mathematics" title="Greek mathematics">Greece</a></li> <li><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Islamic mathematics</a></li> <li><a href="/wiki/History_of_mathematics#Medieval_European_mathematics" title="History of mathematics">Europe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern<br /> institutions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indian_Statistical_Institute" title="Indian Statistical Institute">Indian Statistical Institute</a></li> <li><a href="/wiki/Bhaskaracharya_Pratishthana" title="Bhaskaracharya Pratishthana">Bhaskaracharya Pratishthana</a></li> <li><a href="/wiki/Chennai_Mathematical_Institute" title="Chennai Mathematical Institute">Chennai Mathematical Institute</a></li> <li><a href="/wiki/Institute_of_Mathematical_Sciences,_Chennai" title="Institute of Mathematical Sciences, Chennai">Institute of Mathematical Sciences</a></li> <li><a href="/wiki/Indian_Institute_of_Science" title="Indian Institute of Science">Indian Institute of Science</a></li> <li><a href="/wiki/Harish-Chandra_Research_Institute" title="Harish-Chandra Research Institute">Harish-Chandra Research Institute</a></li> <li><a href="/wiki/Homi_Bhabha_Centre_for_Science_Education" title="Homi Bhabha Centre for Science Education">Homi Bhabha Centre for Science Education</a></li> <li><a href="/wiki/Ramanujan_Institute_for_Advanced_Study_in_Mathematics" title="Ramanujan Institute for Advanced Study in Mathematics">Ramanujan Institute for Advanced Study in Mathematics</a></li> <li><a href="/wiki/Tata_Institute_of_Fundamental_Research" title="Tata Institute of Fundamental Research">TIFR</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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