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Mathematical Intelligence: What We Have that Machines Don't
There's so much talk about the threat posed by intelligent machines that it sometimes seems as though we should surrender to our robot overlords now. But Junaid Mubeen isn't ready to throw in the towel just yet.
As far as he is concerned, we have the edge over machines because of a remarkable system of thought developed over the millennia. It's familiar to us all, but often badly taught and misrepresented in popular discourse - maths.
Computers are brilliant at totting up sums, pattern-seeking and performing, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical superpowers.
As far as he is concerned, we have the edge over machines because of a remarkable system of thought developed over the millennia. It's familiar to us all, but often badly taught and misrepresented in popular discourse - maths.
Computers are brilliant at totting up sums, pattern-seeking and performing, well, computation. For all things calculation, machines reign supreme. But Junaid identifies seven areas of intelligence where humans can retain a crucial edge. And in exploring these areas, he opens up a fascinating world where we can develop our uniquely human mathematical superpowers.
352 pages, Hardcover
Published June 2, 2022
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206 people want to read
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Displaying 1 - 8 of 8 reviews
June 8, 2022
This is a strange one. It's sort of about AI and making it better, and it's sort of about how wonderful mathematics is (and mathematicians are) and why real maths not like the boring stuff we do at school. Whether or not you think this might appeal I would advise skipping the painfully long introduction (36 pages, but it feels like more).
When it comes to the main text, Junaid Mubeen splits down the way humans do things and artificial intelligence doesn't into seven headings: estimation, representations, reasoning, imagination, questioning, temperament and collaboration. The first of these is by far the best, stressing the way that humans don't actually work numerically like computers beyond relatively small numbers. Of course we can do the sums for bigger numbers, but that's where it becomes an effort, where we more naturally deal with approximation.
In each section, Mubeen is looking at what the limitations are for AI, how humans do it and how we can learn from what mathematicians do. This last part was for me by far the least interesting (and that's as someone with a Masters in an applied maths subject) - I can't see it appealing much except to mathematicians or ex-mathematicians like Mubeen.
The bits on AI and its limitations were quite interesting, though there are now a lot of books on this subject - and since reading Elena Esposito's Artificial Communication, I think many such books frame the problem incorrectly. There is some of that here - Mubeen seems to assume it is possible to move from current AI's approach to actual artificial intelligence (and to think that self-driving cars are close to being feasible in the real world, as opposed to California) - but having said that, the seven areas are quite insightful and help underline how far AI is from actual intelligence.
An interesting book in principle, then, but I didn't enjoy it because the mathematical focus didn't work well and was a distraction from the more interesting parts.
When it comes to the main text, Junaid Mubeen splits down the way humans do things and artificial intelligence doesn't into seven headings: estimation, representations, reasoning, imagination, questioning, temperament and collaboration. The first of these is by far the best, stressing the way that humans don't actually work numerically like computers beyond relatively small numbers. Of course we can do the sums for bigger numbers, but that's where it becomes an effort, where we more naturally deal with approximation.
In each section, Mubeen is looking at what the limitations are for AI, how humans do it and how we can learn from what mathematicians do. This last part was for me by far the least interesting (and that's as someone with a Masters in an applied maths subject) - I can't see it appealing much except to mathematicians or ex-mathematicians like Mubeen.
The bits on AI and its limitations were quite interesting, though there are now a lot of books on this subject - and since reading Elena Esposito's Artificial Communication, I think many such books frame the problem incorrectly. There is some of that here - Mubeen seems to assume it is possible to move from current AI's approach to actual artificial intelligence (and to think that self-driving cars are close to being feasible in the real world, as opposed to California) - but having said that, the seven areas are quite insightful and help underline how far AI is from actual intelligence.
An interesting book in principle, then, but I didn't enjoy it because the mathematical focus didn't work well and was a distraction from the more interesting parts.
January 14, 2026
Undirtitillinn er algjört readbait.
Höfundurinn er í raun ekki að færa rök fyrir því að menn hafi einhverjar stærðfræðigáfur sem tölvur geti ekki öðlast. Hann fer þó mjög leynt með þetta og talar á gráu svæði þar til í lokaorðunum, þar sem hann viðurkennir að það sé of sterk staðhæfing. Samt sem áður koma fyrir margir frasar sem bentu til þess að þetta væri það sem hann væri að færa rök fyrir:
"Machine learning is unable to integrate disruptive, pioneering forces into its prognostications of the world."
"It's a huge leap to think that a computer could lead us to classes of numbers not yet conceived. That inventive power is not within the scope of rule-adhering machines." (Hann er þarna að ræða uppgötvun tvinntalnanna).
Svo grefur hann auðvitað upp rök Penrose fyrir því hvernig Gödelsetningarnar sýna fram á að maðurinn geti (samkvæmt lögmálum) gert eitthvað sem engin tölva geti gert.
(Höfundur minnist þó líka á mótrökin fyrir þessu, má gefa honum það).
Ég tel þessar staðhæfingar vera rangar og var mjög efins um að það væri eitthvað vit í þessari bók áður en ég las hana, einmitt vegna undirtitilsins. Rök mín gegn þessu eru einhvernvegin svona:
Hver einasta staðhæfing á forminu:
"Tölvur geta ekki gert X", getur ekki verið rétt. Því ef þú getur lýst eiginleikanum X nægilega vel, þá ertu kominn langleiðina með að geta byggt vél sem hefur eiginleikann X.
Fólk sem setur þessar staðhæfingar fram getur oftast ekki lýst eiginleikanum X.
Aftur á móti, ef við hundsum undirtitilinn og þessar nokkru tæpu staðhæfingar, þá fannst mér bókin allt í lagi. Hún útskýrir vel fyrir almenningi hvað stærðfræði raunverulega snýst um. Það var kannski raunverulega markmið bókarinnar, og undirtitillinn bara settur inn til að selja.
Höfundurinn er í raun ekki að færa rök fyrir því að menn hafi einhverjar stærðfræðigáfur sem tölvur geti ekki öðlast. Hann fer þó mjög leynt með þetta og talar á gráu svæði þar til í lokaorðunum, þar sem hann viðurkennir að það sé of sterk staðhæfing. Samt sem áður koma fyrir margir frasar sem bentu til þess að þetta væri það sem hann væri að færa rök fyrir:
"Machine learning is unable to integrate disruptive, pioneering forces into its prognostications of the world."
"It's a huge leap to think that a computer could lead us to classes of numbers not yet conceived. That inventive power is not within the scope of rule-adhering machines." (Hann er þarna að ræða uppgötvun tvinntalnanna).
Svo grefur hann auðvitað upp rök Penrose fyrir því hvernig Gödelsetningarnar sýna fram á að maðurinn geti (samkvæmt lögmálum) gert eitthvað sem engin tölva geti gert.
(Höfundur minnist þó líka á mótrökin fyrir þessu, má gefa honum það).
Ég tel þessar staðhæfingar vera rangar og var mjög efins um að það væri eitthvað vit í þessari bók áður en ég las hana, einmitt vegna undirtitilsins. Rök mín gegn þessu eru einhvernvegin svona:
Hver einasta staðhæfing á forminu:
"Tölvur geta ekki gert X", getur ekki verið rétt. Því ef þú getur lýst eiginleikanum X nægilega vel, þá ertu kominn langleiðina með að geta byggt vél sem hefur eiginleikann X.
Fólk sem setur þessar staðhæfingar fram getur oftast ekki lýst eiginleikanum X.
Aftur á móti, ef við hundsum undirtitilinn og þessar nokkru tæpu staðhæfingar, þá fannst mér bókin allt í lagi. Hún útskýrir vel fyrir almenningi hvað stærðfræði raunverulega snýst um. Það var kannski raunverulega markmið bókarinnar, og undirtitillinn bara settur inn til að selja.
August 1, 2024
complicated written, definitely something for scolars. But with good views on AI
October 28, 2024
The most effective way to damage a cause is to defend it with faulty arguments and unfortunately this is what happens with this book. The author makes their case so weak that the book ends up giving the false impression that the gap between the human mind and AI is much smaller than what it actually is.
There is a lot of focus on the author personal experience that pushes the arguments in a narrow context. The main points of mathematical thinking are missing. The thorough analysis that allows to break down complex arguments in smaller more understandable arguments, the power of abstraction, the ability to organise our thoughts on multiple levels. All of that gets too little attention. There is no mention of the fact that a similar, highly structured, organisation of our thinking is probably built in our brains in a way that scientists still fail to understand and are unable to reproduce.
How the brain goes from a bunch of neuron spikes to an implicit symbolic system is something that nobody knows, how AI experts failed to implement an equivalent symbolic system into AI is a signal of how far we are from the goal of a real AI. This is something that the author totally ignores.
On the other hand in many passages the books overstates the capabilities of current machine learning and it often takes for granted the marketing claims made by the vendors. All these aspects put together create a misleading picture.
Another arguable point is the excessive space dedicated to the discussion of human biases. It goes so far that a non negligible portion of the book veers off topic.
There is a lot of focus on the author personal experience that pushes the arguments in a narrow context. The main points of mathematical thinking are missing. The thorough analysis that allows to break down complex arguments in smaller more understandable arguments, the power of abstraction, the ability to organise our thoughts on multiple levels. All of that gets too little attention. There is no mention of the fact that a similar, highly structured, organisation of our thinking is probably built in our brains in a way that scientists still fail to understand and are unable to reproduce.
How the brain goes from a bunch of neuron spikes to an implicit symbolic system is something that nobody knows, how AI experts failed to implement an equivalent symbolic system into AI is a signal of how far we are from the goal of a real AI. This is something that the author totally ignores.
On the other hand in many passages the books overstates the capabilities of current machine learning and it often takes for granted the marketing claims made by the vendors. All these aspects put together create a misleading picture.
Another arguable point is the excessive space dedicated to the discussion of human biases. It goes so far that a non negligible portion of the book veers off topic.
April 12, 2025
I was expecting more advanced discussion on the way that machine learning and computational models of intelligence and biological models process information, but the book was mostly a popular science account of mathematics. As that book it certainly is good, a fun read, but if you already are a STEM person or follow a lot of popular science or otherwise understand mathematics then this book probably won't be particularly insightful aside from just being a fun read that gives some space for ones own thoughts to develop. So as a popular science mathematics book 4 stars, but since it didn't live up to the expectation I had, I have to downgrade it to three.
April 8, 2024
Pretty decent book. Though I expect too much.
August 11, 2024
Pretty interesting to read, but a bit too long.
January 4, 2024
tentang kemampuan berpikir dasar yang dimiliki manusia
Displaying 1 - 8 of 8 reviews