Better beware of notions like genius and inspiration; they are a sort of magic wand and should be used sparingly by anybody who wants to see things clearly.(José Ortega y Gasset, “Notes on the novel”)

Does one have to be a genius to do mathematics?

The answer is an emphatic **NO**. In order to make good and useful contributions to mathematics, one does need to work hard, learn one’s field well, learn other fields and tools, ask questions, talk to other mathematicians, and think about the “big picture”. And yes, a reasonable amount of intelligence, patience, and maturity is also required. But one does **not** need some sort of magic “genius gene” that spontaneously generates *ex nihilo* deep insights, unexpected solutions to problems, or other supernatural abilities.

The popular image of the lone (and possibly slightly mad) genius – who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts – is a charming and romantic image, but also a wildly inaccurate one, at least in the world of modern mathematics. We do have spectacular, deep and remarkable results and insights in this subject, of course, but they are the hard-won and cumulative achievement of years, decades, or even centuries of steady work and progress of many good and great mathematicians; the advance from one stage of understanding to the next can be highly non-trivial, and sometimes rather unexpected, but still builds upon the foundation of earlier work rather than starting totally anew. (This is for instance the case with Wiles‘ work on Fermat’s last theorem, or Perelman‘s work on the Poincaré conjecture.)

Actually, I find the reality of mathematical research today – in which progress is obtained naturally and cumulatively as a consequence of hard work, directed by intuition, literature, and a bit of luck – to be far more satisfying than the romantic image that I had as a student of mathematics being advanced primarily by the mystic inspirations of some rare breed of “geniuses”. This “cult of genius” in fact causes a number of problems, since **nobody** is able to produce these (very rare) inspirations on anything approaching a regular basis, and with reliably consistent correctness. (If someone affects to do so, I advise you to be *very* sceptical of their claims.) The pressure to try to behave in this impossible manner can cause some to become overly obsessed with “big problems” or “big theories”, others to lose any healthy scepticism in their own work or in their tools, and yet others still to become too discouraged to continue working in mathematics. Also, attributing success to innate talent (which is beyond one’s control) rather than effort, planning, and education (which are within one’s control) can lead to some other problems as well.

Of course, even if one dismisses the notion of genius, it is still the case that at any given point in time, some mathematicians are faster, more experienced, more knowledgeable, more efficient, more careful, or more creative than others. This does not imply, though, that only the “best” mathematicians should do mathematics; this is the common error of mistaking absolute advantage for comparative advantage. The number of interesting mathematical research areas and problems to work on is vast – far more than can be covered in detail just by the “best” mathematicians, and sometimes the set of tools or ideas that you have will find something that other good mathematicians have overlooked, especially given that even the greatest mathematicians still have weaknesses in some aspects of mathematical research. As long as you have education, interest, and a reasonable amount of talent, there will be some part of mathematics where you can make a solid and useful contribution. It might not be the most glamorous part of mathematics, but actually this tends to be a healthy thing; in many cases the mundane nuts-and-bolts of a subject turn out to actually be more important than any fancy applications. Also, it is necessary to “cut one’s teeth” on the non-glamorous parts of a field before one really has any chance at all to tackle the famous problems in the area; take a look at the early publications of any of today’s great mathematicians to see what I mean by this.

In some cases, an abundance of raw talent may end up (somewhat perversely) to actually be *harmful* for one’s long-term mathematical development; if solutions to problems come too easily, for instance, one may not put as much energy into working hard, asking dumb questions, or increasing one’s range, and thus may eventually cause one’s skills to stagnate. Also, if one is accustomed to easy success, one may not develop the patience necessary to deal with truly difficult problems (see also this talk by Peter Norvig for an analogous phenomenon in software engineering). Talent is important, of course; but how one develops and nurtures it is even more so.

It’s also good to remember that **professional mathematics is not a sport** (in sharp contrast to mathematics competitions). The objective in mathematics is not to obtain the highest ranking, the highest “score”, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications. For these tasks, mathematics needs all the good people it can get.

Further reading:

- “How to be a genius“, David Dobbs, New Scientist, 15 September 2006. [Thanks to Samir Chomsky for this link.]
- “The mundanity of excellence“, Daniel Chambliss, Sociological Theory, Vol. 7, No. 1, (Spring, 1989), 70-86. [Thanks to John Baez for this link.]

## 457 comments

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19 July, 2018 at 2:29 am

My CAREER PLANS after university. – María Alegría[…] [1]“Does one have to be a genius to do maths”, by Terrence Tao […]

9 August, 2018 at 1:59 pm

João CortesI would say that suffering doesn’t enhance any kind of creative thinking, in particular it doesn’t enhance one’s mathematical abilities. But I think that there is a fraction of mathematicians/scientists which are drawn to there fields of work as a response to some kind of suffering, wich diffuses into the way they work resulting in the mentioned dash.

So, even if suffering doesn’t make one a best mathematician, maybe it can make a mathematician in the first place.

23 August, 2018 at 12:34 am

Mike IQAre you Terence Tao? I have just seen him on a news about top highest IQ

Nice to meet you.

6 September, 2018 at 2:13 pm

Meet the partial differential equations tamer - BGSMath[…] famous mathematician, Terry Tao, says that ‘the answer is an emphatic no’. I agree with him. It’s neither necessary nor sufficient. A great deal of math research is just […]

15 September, 2018 at 10:31 am

11th class result 2018Thanks for sharing this :)

15 October, 2018 at 5:03 am

A Hypothesis of Understanding Human Intelligence through Quantum Cognition | Cortical Chauvinism[…] “Does one have to be a genius to do mathematics? The answer is an emphatic no.” – Terry Tao, Fields Medalist (https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/) […]

15 October, 2018 at 5:21 pm

yuvalleventalHello again,

You probably see the backlink to your blog, but I have been thinking of this topic for a while now. It is now my belief that the correct way to understand human abilities is not in terms of genius, it is in terms of the ability to “let go” of measuring people by their intelligence. The more somebody has this ability, the more capable they are. It sounds paradoxical but true, and the reasoning stems from quantum cognition.

I will email it to you if you would like to read it. Hopefully you will enjoy it.

Yuval

https://corticalchauvinism.com/2018/10/15/a-hypothesis-of-understanding-human-intelligence-through-quantum-cognition/

23 October, 2018 at 7:06 am

yuvalleventalAdditionally, you say innate talent is beyond one’s control, that is true. But having less innate talent could prove to be an advantage in the long term. Because autism interfered with my life, I discovered I was vitamin D deficient, and learned a lot about myself in the process https://corticalchauvinism.com/2018/06/11/yuval-levental-vitamin-d-and-autism/

3 December, 2018 at 10:10 am

JozefThank you.

3 December, 2018 at 10:38 pm

Geometry Solving TricksGeometry is fun and even more fun when you score the desired marks. With only a set of rules and theorems to memorize, you are on your way of earning the grades you have always wished for.

18 February, 2019 at 3:51 pm

AnonymousVery nice essay. But…Ramanujan. ;-)

[See my previous comment at https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/#comment-3277 – T.]3 June, 2019 at 5:19 am

yuvalleventalI haven’t commented in a while, but looking back, I think the problem here is that a lot of the advice you give is good, but most people already have heard this advice.

Obviously, this is not a complete list. For instance, as most people know already, diet is very important in success. If one were to eat deep-fried McDonald’s food three times a day, that person would be far worse at math than someone that had whole grains for breakfast and salads for lunch and dinner with light dressing.

In this case, the trick is to look at thousands of years of historical practices, and see if we can find something new that we didn’t think about before.

In the past, there were no refrigerators. So people had to store food by fermenting it. The fermentation process created probiotics, good bacteria that provide nourishment and cognitive benefits.

Only in the past 50 years did the western world abandon probiotics, which suddenly caused a dramatic cognitive decline in America and Europe. In fact, on page 31 of this report, it says that top 5% of American students are only as good as the top 50% of Japanese students (As you definitely know, pickled vegetables are very common in Asian cuisine). http://www.cogsci.ucsd.edu/~deak/classes/EDS115/Stevenson_Stigler_1992.pdf

People can be much better mathematicians and thinkers, but there needs to be an international campaign to bring probiotics back as a daily food. It is a basic human right. My favorites are kombucha, Greek yogurt, and saltwater pickles.

More information: https://corticalchauvinism.com/2019/04/15/yuval-levental-probiotics-prebiotics-and-autism/

27 December, 2019 at 6:39 pm

yuvalleventalI have re-thought your statement “innate talent is beyond one’s control”…

That statement is somewhat true, but far from 100% true. Obviously, everyone has their own set of limitations. But the brain can become more or less powerful to an extent depending on certain actions that we perform: https://en.wikipedia.org/wiki/Neuroplasticity

For instance, in the 1950s, American engineering was the best in the world. Since then, in the following decades, Asian engineering became the best in the world, and American engineering is not very strong today in most areas. The reason is that most American foods became far more processed and less nutritious for various reasons, whereas Asian countries kept eating healthily. This change in lifestyle caused Americans to be far less cognitively capable. It’s not biologically possible that Americans suddenly became far less genetically capable in half a century.

24 March, 2020 at 12:27 am

riderrijuSir what is formality conjecture .

3 May, 2020 at 6:04 am

Hollis WilliamsI think at least in the UK the idea of the ‘lone genius’ is due in part to Isaac Newton but the role of mathematics is really to contribute to mathematics present and future and not ‘to be a genius’. In that sense, Newton’s genius actually had quite a negative impact, as his influence on mathematics in the UK swamped contributions from other good mathematicians from outside for centuries to the point that we still feel the damage perhaps even today several centuries later.

4 July, 2020 at 3:23 am

Who can learn math? – Not So Short Notes[…] Terence Tao on “Does one have to be a genius to do maths?“ […]

21 July, 2020 at 10:39 pm

Rupsa Sahui respect you sir. thank you

23 July, 2020 at 1:26 am

ثرثرة عفوية #5 : الرياضيات، وثقافة العبقرية. - فارس.[…] للمزيد: Does one have to be a genius to do maths? […]

24 July, 2020 at 6:37 am

SanjuVery helpful blog…

We feel more easier if we find something interesting,so the basics should be strong enough in mathematics which will make one to feel comfortable. UCMAS offers Abacus mental math program which helps remove math-related anxiousness through active learning process designed carefully by child development program experts.

3 September, 2020 at 9:44 am

Server Bug Fix: How should I proceed when a (famous) professor says I'm not good enough for research? - TECHPRPR[…] perceive as being ‘geniuses’ who actually did harm to their subject. Please read the blog post by Terry Tao on this […]

11 November, 2020 at 2:54 am

BrunoOut of 10 000 PhD a year, 1 will get the field medal.

The chances for the 50 people who get the golden medal at IMO to get this field medal, including all those who wont study math at research level, is 1 in 100 or 100 times more than the PhD persons

But it appears then out of 2/3 people who got a perfect score, 8% will get a Medal Fields including the only woman who got it.

IMO being a math IQ test (very restricted knowledge and very astute thinking required), it shows an extreme predictive power of math IQ to math research potential

11 November, 2020 at 9:37 am

Anonymous (@Dinostraurio)nice observation; let us see it the other way around (which I think is the point of Terence): there are 10K new mathematicians every year which will participate with at least one theorem published in a journal.

9.999K of those are not considered genius by the IMU.

9.95K will not even get a gold medal in the IMO…

Furthermore, if you find one of them in the street, you may not even give a penny for him :)

Besides Terence —the only genius in this discussion— we, the most majority of mathematicians alive, are normal street people who decided to have a challenging profession, not genius at all.

23 November, 2020 at 3:56 am

AnonymousDo “the most majority of mathematicians” contribute anything new (and quite important as well) to math?

23 November, 2020 at 9:07 am

AnonymousCurrently “unimportant” mathematical contribution may become “important” in the future.

24 November, 2020 at 10:30 pm

AnonymousRight, this happened in the history too. But what I was mainly asking was do they have the ability to contribute new things while not being genius, mostly with the help of hardwork?

26 November, 2020 at 5:31 am

Anonymous (@Dinostraurio)Exactly, that is the hole point of the discussion here; most of the theorems proved and published out there are the result of hard work, not of a genius idea…

30 December, 2020 at 8:34 am

Mike SmithI am in a PhD science program and have been told that my GPA isn’t high enough to continue. I can graduate with a master’s, but I need to pay the rest of the funds. How can I make up for this pitfall, while being able to follow my passions?

30 December, 2020 at 10:34 am

AnonymousGet a job, and follow your passion in your spare time.

30 December, 2020 at 10:40 am

Mike SmithCitizen scientist then, it is

28 February, 2021 at 1:20 pm

fatherofdragons23Grothendieck told deligne that, math is not a sport.

2 March, 2021 at 1:22 am

DanielHello, Professor Tao. I’m an Engineering student in my second year, but with a very avid interest in higher mathematics. Is there any more efficient method of self-study and also is it a good idea to restrict my study to certain fields only at this stage?

2 March, 2021 at 12:33 pm

NikDo you think it is possible for anyone (with normal mental capacity) to become a mathematician given dedication, hard work, patience, etc.?

19 March, 2021 at 7:44 am

YuvalHello, I have done a lot of research on diet and intelligence, and the results that I discovered are astounding. Essentially, anti-nutrients in food and artificial sugars/fibers dramatically lower intelligence. These foods are all too common in America. I would say that these discoveries could even change the world as a whole for the better.

https://corticalchauvinism.com/2020/07/27/the-best-diet-plan-for-autistic-people-and-for-everyone-else/

https://corticalchauvinism.com/2021/03/15/opposition-to-artificial-sugars-impact-on-autism-and-general-health/

13 July, 2021 at 12:07 pm

CalcuquackI am also a member of the cult of geniuses and the cult of prime numbers(tm).

28 July, 2021 at 10:57 am

Chris Smith“The popular image of the lone (and possibly slightly mad) genius – who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts…”

That is true in some cases. John Nash developed Nash Equilibrium using this method as a graduate student. Some of the professors thought that he wouldn’t be able to initially succeed.

28 July, 2021 at 11:43 am

AnonymousOther famous examples are Galois and Ramanujan.

28 July, 2021 at 5:25 pm

AnonymousNash wasn’t lone at the time though—he was in contact with the other experts in the field like von Neumann. He also wasn’t mad or suffering quite yet.

29 July, 2021 at 8:08 am

AnonymousHe wasn’t schizophrenic yet, but many of his fellow graduate students thought he was very strange (see A Beautiful Mind by Sylvia Nasar). He got along with some faculty members, but was still an outsider compared to the faculty’s expectations as a whole.