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	<id>https://www.ellipticcurve.info/Soft_math/history?feed=atom</id>
	<title>Soft math - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://www.ellipticcurve.info/Soft_math/history?feed=atom"/>
	<link rel="alternate" type="text/html" href="https://www.ellipticcurve.info/Soft_math/history"/>
	<updated>2026-06-20T09:17:21Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=208&amp;oldid=prev</id>
		<title>Rational Point: /* General recommendations to mitigate */ w/</title>
		<link rel="alternate" type="text/html" href="https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=208&amp;oldid=prev"/>
		<updated>2025-01-05T17:33:41Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;General recommendations to mitigate: &lt;/span&gt; w/&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:33, 5 January 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l11&quot;&gt;Line 11:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 11:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Cryptography is a martial art&amp;#039;&amp;#039;&amp;#039; which cannot be practiced properly without the discipline of simple rigorous definitions and hard, step-by-step proofs, and accordingly all mathematical concepts which are employed in the service of [[strong cryptography]] must be brought into the jurisdiction of the martial arts as such.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Cryptography is a martial art&amp;#039;&amp;#039;&amp;#039; which cannot be practiced properly without the discipline of simple rigorous definitions and hard, step-by-step proofs, and accordingly all mathematical concepts which are employed in the service of [[strong cryptography]] must be brought into the jurisdiction of the martial arts as such.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Our goals and objectives here are to overcome heavy resistance, espionage and well-armed campaigns of disinformation from entrenched insiders of the “soft math” camps in order to simplify and strengthen the definitions and make the theorems more rigorous and provable for engineering applications outside a peculiar academic sub-discipline of advanced algebraic group theory which has “gone soft,” so that we can better understand from an outsider perspective the group structure of elliptic curves over finite fields &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;from &lt;/del&gt;a point of view of establishing and maintaining provable security properties for cryptographic applications.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Our goals and objectives here are to overcome heavy resistance, espionage and well-armed campaigns of disinformation from entrenched insiders of the “soft math” camps in order to simplify and strengthen the definitions and make the theorems more rigorous and provable for engineering applications outside a peculiar academic sub-discipline of advanced algebraic group theory which has “gone soft,” so that we can better understand from an outsider perspective the group structure of elliptic curves over finite fields &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;with &lt;/ins&gt;a point of view of establishing and maintaining provable security properties for cryptographic applications.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rational Point</name></author>
	</entry>
	<entry>
		<id>https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=207&amp;oldid=prev</id>
		<title>Rational Point: entrenched academia</title>
		<link rel="alternate" type="text/html" href="https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=207&amp;oldid=prev"/>
		<updated>2025-01-05T17:30:34Z</updated>

		<summary type="html">&lt;p&gt;entrenched academia&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:30, 5 January 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Soft Math ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soft math&amp;#039;&amp;#039;&amp;#039; is characterized by the use of mathematics-oriented computer &amp;#039;&amp;#039;&amp;#039;software&amp;#039;&amp;#039;&amp;#039;, and has been used to collect heuristic or statistical evidence for may conjectures such as the [[Riemann hypothesis]] and the [[Birch and Swinnerton-Dyer conjecture]].&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soft math&amp;#039;&amp;#039;&amp;#039; is characterized by the use of mathematics-oriented computer &amp;#039;&amp;#039;&amp;#039;software&amp;#039;&amp;#039;&amp;#039;, and has been used to collect heuristic or statistical evidence for may conjectures such as the [[Riemann hypothesis]] and the [[Birch and Swinnerton-Dyer conjecture]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l5&quot;&gt;Line 5:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Much of the “soft math“ we are presented with in abstract algebra or group theory journal articles and so forth has become too abstract, advanced and theoretical with vague definitions leaving behind the formal proofs for the initial simplest concrete results upon which it is based. This is what happened at the [[monstrous moonshine]] camp.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Much of the “soft math“ we are presented with in abstract algebra or group theory journal articles and so forth has become too abstract, advanced and theoretical with vague definitions leaving behind the formal proofs for the initial simplest concrete results upon which it is based. This is what happened at the [[monstrous moonshine]] camp.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Cryptography is a martial art&#039;&#039;&#039; which cannot be practiced properly without the discipline of simple rigorous definitions and hard, step-by-step proofs, and accordingly all mathematical concepts which are employed in the service of [[strong cryptography]] must be brought into the jurisdiction of the martial &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;art &lt;/del&gt;as such.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;=== General recommendations to mitigate ===&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Cryptography is a martial art&#039;&#039;&#039; which cannot be practiced properly without the discipline of simple rigorous definitions and hard, step-by-step proofs, and accordingly all mathematical concepts which are employed in the service of [[strong cryptography]] must be brought into the jurisdiction of the martial &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;arts &lt;/ins&gt;as such&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Our goals and objectives here are to overcome heavy resistance, espionage and well-armed campaigns of disinformation from entrenched insiders of the “soft math” camps in order to simplify and strengthen the definitions and make the theorems more rigorous and provable for engineering applications outside a peculiar academic sub-discipline of advanced algebraic group theory which has “gone soft,” so that we can better understand from an outsider perspective the group structure of elliptic curves over finite fields from a point of view of establishing and maintaining provable security properties for cryptographic applications&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rational Point</name></author>
	</entry>
	<entry>
		<id>https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=204&amp;oldid=prev</id>
		<title>Rational Point: jurisdiction of the martial art</title>
		<link rel="alternate" type="text/html" href="https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=204&amp;oldid=prev"/>
		<updated>2025-01-05T14:00:12Z</updated>

		<summary type="html">&lt;p&gt;jurisdiction of the martial art&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 14:00, 5 January 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In some ways it may be seen as “applied” rather than pure mathematics which would be based on formal definitions and proofs for all key terms and theorems based on them, even if it isn’t “applied” as such to practical use “out on the farm” as it were.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;In some ways it may be seen as “applied” rather than pure mathematics which would be based on formal definitions and proofs for all key terms and theorems based on them, even if it isn’t “applied” as such to practical use “out on the farm” as it were.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Much of the “soft math“ we are presented with in abstract algebra or group theory journal articles and so forth has become too abstract, advanced and theoretical with vague definitions leaving behind the formal proofs for the initial simplest concrete results upon which it is based.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Much of the “soft math“ we are presented with in abstract algebra or group theory journal articles and so forth has become too abstract, advanced and theoretical with vague definitions leaving behind the formal proofs for the initial simplest concrete results upon which it is based&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. This is what happened at the [[monstrous moonshine]] camp.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;Cryptography is a martial art&#039;&#039;&#039; which cannot be practiced properly without the discipline of simple rigorous definitions and hard, step-by-step proofs, and accordingly all mathematical concepts which are employed in the service of [[strong cryptography]] must be brought into the jurisdiction of the martial art as such&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rational Point</name></author>
	</entry>
	<entry>
		<id>https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=203&amp;oldid=prev</id>
		<title>Rational Point: soft math defined</title>
		<link rel="alternate" type="text/html" href="https://www.ellipticcurve.info/index.php?title=Soft_math&amp;diff=203&amp;oldid=prev"/>
		<updated>2025-01-05T09:21:31Z</updated>

		<summary type="html">&lt;p&gt;soft math defined&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Soft math&amp;#039;&amp;#039;&amp;#039; is characterized by the use of mathematics-oriented computer &amp;#039;&amp;#039;&amp;#039;software&amp;#039;&amp;#039;&amp;#039;, and has been used to collect heuristic or statistical evidence for may conjectures such as the [[Riemann hypothesis]] and the [[Birch and Swinnerton-Dyer conjecture]].&lt;br /&gt;
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In some ways it may be seen as “applied” rather than pure mathematics which would be based on formal definitions and proofs for all key terms and theorems based on them, even if it isn’t “applied” as such to practical use “out on the farm” as it were.&lt;br /&gt;
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Much of the “soft math“ we are presented with in abstract algebra or group theory journal articles and so forth has become too abstract, advanced and theoretical with vague definitions leaving behind the formal proofs for the initial simplest concrete results upon which it is based.&lt;/div&gt;</summary>
		<author><name>Rational Point</name></author>
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